Mensuration

Problem 301

Find the area of the region bound by the following equations: $y=6 x+6, \quad y=0, \quad x=3 \text { and } x=7$

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Problem 302

Determine the area of the given square. $A=B * H$

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Problem 303

9. A cardboard box measures 40 cm by 40 cm by 30 cm . Calculate 6 length of the space diagonal, to the nearest centimetre.

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Problem 304

$\text{Given a triangle with side lengths: } a = 12 \, \text{m}, \, b = 7.5 \, \text{m}, \, c = 8 \, \text{m}.$ \text{Find the perimeter and area of this triangle.}

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Problem 305

A school playground is in the shape of a rectangle 400 feet long and 200 feet wide. If fencing costs $\$ 19$ per yard, what will it cost to place fencing around the playground? \\square$

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Problem 306

4) A person throws a ball with an initial velocity of 15 meters $/ \mathrm{sec}$ at an angle of $20^{\circ}$ above the grd How far from the person will the ball land? Horizo

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Problem 307

The graph shows the map of a park with sport fields, play area, and forest label. The entrance of the park is at the origin. The segments represent a walking path. The value on each axis is in hundreds of feet.
The triangular section represents a forest along the walking path.
Which value represents the area of the forest? A. 160,000 square feet B. 480,000 square feet C. 560,000 square feet D. 640,000 square feet

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Problem 308

Area involving rectangles and triangles
A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer. $\square$

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Problem 309

7 of 15
5E: Changing the Area hink back to the original description of the ectangular sandbox. e were told that Alexa has a rectangular sandbox lat measures 8 ft long and 6 ft wide. She wants to crease the area to $120 \mathrm{ft}^{2}$ by increasing the width d length by the same amount.
Based on the description and your calculations, fill in the table below. Just enter the numbers in the boxes. $\div$ 勘 Present Gallery React (ㄷ) ings

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Problem 310

21. You have a 1200 -foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area and the dimensions of this largest rectangular enclosure? \begin{tabular}{|l|l|} \hline $\square$ \\ $\square$ \end{tabular}

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Problem 311

A parallelogram has sides of lengths 8 and 7 , and one angle is $38^{\circ}$ . What is the length of the smaller diagonal? length $=$ $\square$ units
What is the length of the longer diagonal? length = $\square$ units
Enter your answer as a number; your answer should be accurate to 3 decimal plo

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Problem 312

If each square in the grid represents a square foot, then which statements are true? Choose allthatare correct A. Each bookshelf has a perimeter less than 8 feet. B. The perimeter of the s of a is more than 12 feet. C. The perimeter of the entertainment center is less than 14 feet. D. The perimeter of the chair is a bout 8.5 feet. E. The perimeter of the area rug is about 20 feet.

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Problem 313

A rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. $V=$ $\square$ (Simplify your answer. Do not factor.)

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Problem 314

A truck is filling a container with sand. The container is in the shape of a rectangular prism as pictured.
The truck puts $40 \mathrm{~m}^{3}$ of sand in the container. How much more sand is needed to completely fill the container? A $14 \mathrm{~m}^{3}$
B $68 \mathrm{~m}^{3}$ c $108 \mathrm{~m}^{3}$
D $148 \mathrm{~m}^{3}$
MTH1W

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Problem 315

Line $\ell$ has equation $y=x-2$ . Find the distance between $\ell$ and the point $R(-5,0)$ . Round your answer to the nearest tenth.

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Problem 316

Part 2 of 2
Sheila is building an addition to a house. The points $\mathrm{E}\left(-1 \frac{1}{2},-2 \frac{1}{2}\right), \mathrm{F}\left(4 \frac{1}{2},-2 \frac{1}{2}\right), \mathrm{G}\left(4 \frac{1}{2}, 3 \frac{1}{2}\right)$ , and $\mathrm{H}\left(-1 \frac{1}{2}, 3 \frac{1}{2}\right)$ are the points she plotted on a coordinate plane to draw the room plan. What is the shape of the addition to the house? What is the perimeter in units?

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Problem 317

A blueprint is drawn using a scale of $\frac{2 \mathrm{inm}}{25 \mathrm{ft}}$ . What length is represented by 1 mm ?
50 ft 12.5 ft 10.5 ft
23 ft

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Problem 318

A blueprint is drawn using a scale of $\frac{2 \mathrm{inm}}{25 \mathrm{ft}}$ . What length is represented by 1 mm ?
50 ft 12.5 ft 10.5 ft
23 ft

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Problem 319

Heather has 360 meters of fencing and wishes to enclose a rectangular field. Suppose that a side length (in meters) of the field is $x$ , as shown below. (a) Find a function that gives the area $A(x)$ of the field (in square meters) in terms of $x$ . $A(x)=$ $\square$ (b) What side length $x$ gives the maximum area that the field can have?
Side length $x$ : $\square$ meters (c) What is the maximum area that the field can have?
Maximum area: $\square$ square meters

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Problem 320

A fish tank is in the shape of a cube. The volume of the tank is 64 cubic feet. What is the width, in inches, of one side of the fish tank?
192 inches 48 inches 96 inches 256 inches

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Problem 321

Find the area of the figure. (Sides meet at right angles.) $\square$ $y d^{2}$ Gheck O 2024 McGraw Hill LLC. Al

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Problem 322

Find the area of this parallelogram. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. $\square$ in

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Problem 323

The ratio of the side length of a square to the square's perimeter is always 1 to 4 . Peter drew a square with a perimeter of 28 inches.
What is the side length of the square Peter drew?

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Problem 324

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. What are the dimensions of her scale drawing using $3 \mathrm{~cm}$ for every $4 \mathrm{ft}$ ?

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Problem 325

A $12.875-\mathrm{m}$ fence is one side of a rectangle. With $45.625 \mathrm{~m}$ left for the other sides, find the longer dimension.

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Problem 326

Find the area of parallelogram $ABCD$ with sides 6 and 4 units and an angle of 125 degrees. Compare it to 24.

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Problem 327

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. With a scale of $3 \mathrm{cm}$ for $4 \mathrm{ft}$ , find the drawing's dimensions.

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Problem 328

A scale drawing shows a closet measuring $4.4 \mathrm{~cm}$ by $3.2 \mathrm{~cm}$ . With a scale of $2 \mathrm{~cm}$ to $1 \mathrm{~m}$ , find the actual area.

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Problem 329

A rectangle has dimensions $10 \mathrm{~cm}$ by $8 \mathrm{~cm}$ . If length increases by $60\%$ , find width's percentage change if: (a) perimeter stays the same. (b) area stays the same.

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Problem 330

Calcula cuántos rollos de material necesita comprar para insonorizar 4 paredes de 2 m x 2.2 m, considerando una puerta de 0.8 m.

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Problem 331

Calcula el volumen de un archivador de $150 \mathrm{~cm}$ alto, $55 \mathrm{~cm}$ ancho y $60 \mathrm{~cm}$ fondo en m³.

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Problem 332

Find the radius of a sphere with volume $4.5 \mathrm{~m}^{3}$ using the formula $V=\frac{4}{3} \pi r^{3}$ .

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Problem 333

Find the length $L$ and width $W$ (with $W \leq L$ ) of a rectangle with perimeter 28 that maximizes area. What is the max area?

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Problem 334

Calculate the area of quadrilateral $ABCD$ with vertices $A(0,2)$ , $B(4,7)$ , $C(8,2)$ , $D(4,3)$ .

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Problem 335

Calculate the area of a parallelogram with base 6 inches and height 3 inches. Use the formula: Area = base × height = $6 \times 3$ .

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Problem 336

Find the area of a sector with radius 2 cm and central angle 90°, where OE = OF.

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Problem 337

Yair added sawdust to a toilet. The seat is $0.4 \mathrm{~m}$ above ground and the pit bottom is $1.5 \mathrm{~m}$ below.
1. Find the distance from the toilet seat to the pit bottom in $\mathrm{m}$ .
2. Calculate the height change of the sawdust from the seat to the pit bottom.

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Problem 338

Find the distance between Natasha's beagle at $\frac{25}{4}$ meters and her labrador at $\frac{51}{20}$ meters.

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Problem 339

A tank is 4.5 m long, 3.5 m wide, and 2.8 m deep. Water is pumped at 6500 L/h. After 3 hours, what is the water level from the top?

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Problem 340

What is the total cost of a rectangular plot measuring $1200 \mathrm{~m} \times 900 \mathrm{~m}$ if 1 hectare costs R5 200,00?

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Problem 341

Find the length of a side of square ABCD if its area is 89 cm². What is $\widehat{x}$ ?

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Problem 342

Calculate the volume of a hole measuring $11.0 \mathrm{~m} \times 14.5 \mathrm{~m} \times 4.0 \mathrm{~m}$ and a truck bed $4 \mathrm{~m} \times 3 \mathrm{~m} \times 2.0 \mathrm{~m}$ . How many trips needed?

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Problem 343

Find the area of the tiled walkway around a $24 \mathrm{ft} \times 12 \mathrm{ft}$ pool with a $2 \mathrm{ft}$ wide border.

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Problem 344

Find the map length of a road that is $3 \mathrm{~km}$ long, with a scale of $1: 120000$ . Answer in $\mathrm{cm}$ .

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Problem 345

Find the range of the actual area of a rectangle with width $3.0 \mathrm{~cm}$ and length $8.0 \mathrm{~cm}$ .

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Problem 346

Find the maximum absolute error for the measurements of an 8-sided polygon with given sides: $GF = 4cm$ , $FE = 3cm$ , $DC = 6cm$ , $CB = 8cm$ .

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Problem 347

In an 8-sided polygon $ABCDEFGH$ with rectangles $ABCD$ and $EFGH$ , find:
(a) max error in cm. (b) min area of rectangle $ABCD$ . (c) min area of rectangle $EFGH$ . (d) range of actual area $x$ in cm².

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Problem 348

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length $s$ .

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Problem 349

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 350

Find the length of the latus rectum and the parabolic arc for the parabola given by $x^{2}=4 a y$ .

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Problem 351

Find the length and width of a rectangular garden with area $96 \mathrm{~m}^{2}$ and perimeter $40 \mathrm{~m}$ .

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Problem 352

Find the equation of line $O A$ , show $A$ is $(16,-8)$ , and calculate area of trapezium $O A B C$ .

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Problem 353

Find the maximum load $P$ for an 8m beam with I section dimensions and stress limit of 340 MPa.

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Problem 354

Find the volume of a donut box with length 9 in, width 4 in, and height 3 in: $V = l \times w \times h$ .

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Problem 355

Find the volume of a donut box with dimensions: length = 9 in, width = 4 in, height = 3 in. Use $V = l \times w \times h$ .

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Problem 356

Find the volume of a rectangular prism with a base area of 20 unit cubes and 4 layers high.

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Problem 357

What is the volume of a rectangular prism with a base area of 20 unit cubes and a height of 4 layers?

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Problem 358

Penelope's Pizzeria has a pizza box volume of 12 cubic units. Which dimensions are possible? A. $1 \times 12 \times 1$ B. $3 \times 2 \times 2$ C. $6 \times 3 \times 1$

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Problem 359

What is the volume of a rectangular prism with a base area of 20 unit cubes and a height of 4 layers?

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Problem 360

Astiton compares two peanut boxes: Box 1 (base 14 in², height 7 in) and Box 2 (105 in³). Which has more volume?

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Problem 361

Astiton wants to buy the box of peanuts with the most volume. Compare Box 1 ( $14 \times 7$ ) and Box 2 ( $105$ ). Which is larger?

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Problem 362

Ashton needs to choose between two peanut boxes. Box \#1 has a volume of $14 \times 7 = 98$ cubic inches. Box \#2 is 105 cubic inches. Which box is larger?

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Problem 363

Locate points of rectangle $ABCD$ at $A(2,2), B(2,-1), C(-1,-1), D(-1,2)$ , then find its perimeter and area.

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Problem 364

Find the perimeter of a pentagon with sides 14, 12, 10, 8, and 6 inches using the expression $P = 14 + 12 + 10 + 8 + 6$ .

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Problem 365

César siembra un terreno cuadrado de 6 m en 20 min. ¿Cuánto tardará en sembrar uno de 12 m de lado?

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Problem 366

Punctele coliniare $A, B$ și $C$ au $B C=2 A C$ . Dacă $M$ și $N$ sunt mijloacele segmentelor $A C$ și $C B$ cu $M N=9 \mathrm{~cm}$ , găsește lungimea lui $A C$ : a) $3 \mathrm{~cm}$ ; b) $6 \mathrm{~cm}$ ; c) $18 \mathrm{~cm}$ .

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Problem 367

Hitung luas bilik dalam $\mathrm{cm}^{2}$ jika 250 jubin berukuran $6.096 \times 10^{2} \mathrm{~mm}$ dan $3.048 \times 10^{2} \mathrm{~mm}$ .

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Problem 368

Find a formula for the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 369

Find the volume of a right cone with a base diameter of $9.5 \mathrm{~cm}$ and a height of $16 \mathrm{~cm}$ .

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Problem 370

In a pipeline with a 30 cm diameter and water speed of 1.5 m/s, find the speed at a 1 cm diameter.

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Problem 371

The office floor plan is at a scale of $1:20$ . Find the actual length for $96 \mathrm{~cm}$ and pantry area in $\mathrm{cm}^{2}$ for $4.8 \mathrm{~m}^{2}$ .

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Problem 372

In square $ABCD$ , area equals the sum of areas of triangles $ABE$ and $DCE$ . If $AB=6$ , find $CE$ . (a) 5 (b) 6 (c) 2 (d) 3 (e) 4

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Problem 373

In square $ABCD$ with $AB=6$ , the area equals the sum of triangles $ABE$ and $DCE$ . Find length of $CE$ .

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Problem 374

Find the area $x$ of hexagon $ABCDEF$ with rectangle $ABCD$ where $AB=9$ cm, $BC=16$ cm, $AE=8$ cm, and $FG=3$ cm.

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Problem 375

Berechne Volumen und Oberfläche einer Pyramide mit Grundfläche $a=15 \mathrm{~cm}, b=12 \mathrm{~cm}, h=20 \mathrm{~cm}$ .

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Problem 376

Clarence's garden is 20 ft by 40 ft. How many 4-yard fencing packages do they need for the perimeter?

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Problem 377

Berechne das Volumen und die Oberfläche eines Quaders mit $a=4 \mathrm{~cm}, b=6 \mathrm{~cm}, c=12 \mathrm{~cm}$ .

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Problem 378

Calculate the volume and surface area of a cube with side length 3 units. Use $V = s^3$ and $A = 6s^2$ .

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Problem 379

Find the volume of a cuboid with dimensions 3, 3, and 4 units: $V = l \times w \times h$ .

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Problem 380

What does the coefficient 7 represent in a rectangle with width $x$ and length $7x$ ? A. Length is 7 times width. B. Area is 7. C. Width is 7 times length. D. Length is 7.

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Problem 381

Thando's bag is 35cm x 35cm x 30cm. How many 27cm x 27cm x 3.5cm pizza boxes fit in it? After a 15% size increase, can they still fit?

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Problem 382

Elena has a rectangular aquarium with height $1 \frac{3}{4} \mathrm{ft}$ . If the painted area is $5 \frac{5}{6} \mathrm{ft}^{2}$ , find the length.

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Problem 383

Find the volume of Lin's aquarium with dimensions $\frac{7}{2} \mathrm{ft}$ (length), $\frac{4}{3} \mathrm{ft}$ (width), and $\frac{3}{2} \mathrm{ft}$ (height).

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Problem 384

Calculați aria dreptunghiului $A B C D$ având $A C=6 \mathrm{~cm}$ și $\angle D O C=120^{\circ}$ . Care este aria?

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Problem 385

A rectangular prism A has dimensions: length = $4 \mathrm{~cm}$ , width = $3 \mathrm{~cm}$ , height = $2 \mathrm{~cm}$ .
a) How many cubes fit along the length?
b) How many cubes fit along the width?
c) How many layers of cubes?
d) What is the volume in cubes?

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Problem 386

Xavier's papaya trees cover $370 \mathrm{~m}^{2}$ . The perimeter for pineapple trees is $84 \mathrm{~m}$ . Find their area.

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Problem 387

Find the length of a rectangular fishpond with a perimeter of $62 \mathrm{~m}$ and length 3 times its width.

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Problem 388

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 389

What is the area of this figure? $\square$ square meters Submit

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Problem 390

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm . If the area of printed material on the poster is fixed at $1,536 \mathrm{~cm}^{2}$ , find the dimensions (in cm ) of the poster with the smallest area.

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Problem 391

\begin{tabular}{|c|c|} \hline & $V=\frac{1}{3} b h \quad$ for $b$ \\ \hline \end{tabular}

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Problem 392

Плошадь параллелограмма Вариант 2 №1. Высота параллелограмма равна 9 cm , а основание - 14 cm . Найдите площадь параллелограмма. N22. Найдите площадь параллелограмма, изображенного на рисунке 1. №3. Найдите площадь параллелограмма, изображенного на рисунке 2 , если размер клетки $1 \times 1.8$ №4. Площадь параллелограмма равна $42 \mathrm{~m}^{2}$ , а основание - 7 м. Найдите высоту параллелограмма. №5. На рисунке 3 изображен параллелограмм $\mathrm{ABCD}, \mathrm{AB}=6 \mathrm{~cm}$ , высоты BE и DF равны по 4 и 8 cm . Найдите сторону AD. №6. По данньмм рисунка 4 найдите площадь параллелограмма.
Рис. 1.
Рис.2.
Рис. 3. c
Рис.4.

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Problem 393

The radius, $R$ , of a sphere is 9.3 m . Calculate the sphere's volume, $V$ . Use the value 3.14 for $\pi$ , and round your answer to the nearest tenth. (Do not round any intermediate computations.) $V=\square \mathrm{m}^{3}$

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Problem 394

3. Kyle and Mark started at the same location. Kyle traveled 5 miles due east, while Mark traveled 3 miles due West. How far apart are they? (A) 2 miles (B) 8 miles (C) $\mathbf{1 5}$ miles (D) 12 miles

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Problem 395

Joe has a barn in his back yard. Figure A is a diagram representing the side view of the barn.
Figure A
Find the perimeter of the side of the barn.
The perimeter of the side of the barn is $\square$ $f t$ . Find the area of the side of the barn.
The area of the side of the barn is $\square$ sq. $f t$ .

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Problem 396

Figure A: 3-Dimensional Figu (b) $18 \mathrm{mins} x$

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Problem 397

7) A triangular parcel of land has sides lengths of 60 meters, 70 meters, and 82 meters. Find the area of the parcel of land.

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Problem 398

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $\$ 10$ per linear foot to install and the farmer is not willing to spend more than $\$ 7000$ , find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)

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Problem 399

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $\$ 8$ per linear foot to install and the farmer is not willing to spend more than $\$ 4000$ , find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)

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Problem 400

Площадь квадрата и прямоугольника Вариант 2 1.В прямоугольнике одна сторона равна 10 , другая сторона равна 14. Найдите площадь прямоугольника.
2. Найти сторону квадрата, если площадь равна: а) $289 \mathrm{~m}^{2}$ ; б) $\frac{4}{5} \mathrm{CM}^{2}$ в) 12 дм $^{2}$ 3.В прямоугольнике одна сторона равна 14 , периметр равен 54 . Найдите площадь прямоугольника.
4. Периметр квадрата равен 20 cm . Найдите его площадь. 5.Найдите площадь прямоугольника, если его периметр равен 58 и одна сторона на 5 больше другой.
6. Пол комнаты, имеюощей форму прямоугольника со сторонами 4 m и 7 m , требуется покрыть паркетом из прямоугольных дощечек со сторонами 7 cm и 20 cm . Сколько потребуется таких дощечек?

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1 2 3 4 5 6 7 ...14

Mensuration

Problem 301

Find the area of the region bound by the following equations: y=6x+6,y=0,x=3 and x=7y=6 x+6, \quad y=0, \quad x=3 \text { and } x=7y=6x+6,y=0,x=3 and x=7

Problem 302

Determine the area of the given square. A=B∗HA=B * HA=B∗H

Problem 303

9. A cardboard box measures 40 cm by 40 cm by 30 cm . Calculate 6 length of the space diagonal, to the nearest centimetre.

Problem 304

Given a triangle with side lengths: a=12 m, b=7.5 m, c=8 m.\text{Given a triangle with side lengths: } a = 12 \, \text{m}, \, b = 7.5 \, \text{m}, \, c = 8 \, \text{m}.Given a triangle with side lengths: a=12m,b=7.5m,c=8m. \text{Find the perimeter and area of this triangle.}

Problem 305

A school playground is in the shape of a rectangle 400 feet long and 200 feet wide. If fencing costs $19\$ 19$19 per yard, what will it cost to place fencing around the playground? \ \square$

Problem 306

4) A person throws a ball with an initial velocity of 15 meters /sec/ \mathrm{sec}/sec at an angle of 20∘20^{\circ}20∘ above the grd How far from the person will the ball land? Horizo

Problem 307

Problem 308

Area involving rectangles and trianglesA right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer. □\square□

Problem 309

Problem 310

21. You have a 1200 -foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area and the dimensions of this largest rectangular enclosure? \begin{tabular}{|l|l|} \hline□\square□ \\ □\square□ \end{tabular}

Problem 311

Problem 312

Problem 313

A rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. V=V=V= □\square□ (Simplify your answer. Do not factor.)

Problem 314

Problem 315

Line ℓ\ellℓ has equation y=x−2y=x-2y=x−2. Find the distance between ℓ\ellℓ and the point R(−5,0)R(-5,0)R(−5,0). Round your answer to the nearest tenth.

Problem 316

Problem 317

A blueprint is drawn using a scale of 2inm25ft\frac{2 \mathrm{inm}}{25 \mathrm{ft}}25ft2inm​. What length is represented by 1 mm ?50 ft 12.5 ft 10.5 ft23 ft

Problem 318

A blueprint is drawn using a scale of 2inm25ft\frac{2 \mathrm{inm}}{25 \mathrm{ft}}25ft2inm​. What length is represented by 1 mm ?50 ft 12.5 ft 10.5 ft23 ft

Problem 319

Problem 320

A fish tank is in the shape of a cube. The volume of the tank is 64 cubic feet. What is the width, in inches, of one side of the fish tank?192 inches 48 inches 96 inches 256 inches

Problem 321

Find the area of the figure. (Sides meet at right angles.) □\square□ yd2y d^{2}yd2 Gheck O 2024 McGraw Hill LLC. Al

Problem 322

Find the area of this parallelogram. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. □\square□ in

Problem 323

The ratio of the side length of a square to the square's perimeter is always 1 to 4 . Peter drew a square with a perimeter of 28 inches.What is the side length of the square Peter drew?

Problem 324

Francesca's mural is 12ft12 \mathrm{ft}12ft high and 135ft135 \mathrm{ft}135ft long. What are the dimensions of her scale drawing using 3 cm3 \mathrm{~cm}3 cm for every 4ft4 \mathrm{ft}4ft?

Problem 325

A 12.875−m12.875-\mathrm{m}12.875−m fence is one side of a rectangle. With 45.625 m45.625 \mathrm{~m}45.625 m left for the other sides, find the longer dimension.

Problem 326

Find the area of parallelogram ABCDABCDABCD with sides 6 and 4 units and an angle of 125 degrees. Compare it to 24.

Problem 327

Francesca's mural is 12ft12 \mathrm{ft}12ft high and 135ft135 \mathrm{ft}135ft long. With a scale of 3cm3 \mathrm{cm}3cm for 4ft4 \mathrm{ft}4ft, find the drawing's dimensions.

Problem 328

A scale drawing shows a closet measuring 4.4 cm4.4 \mathrm{~cm}4.4 cm by 3.2 cm3.2 \mathrm{~cm}3.2 cm. With a scale of 2 cm2 \mathrm{~cm}2 cm to 1 m1 \mathrm{~m}1 m, find the actual area.

Problem 329

A rectangle has dimensions 10 cm10 \mathrm{~cm}10 cm by 8 cm8 \mathrm{~cm}8 cm. If length increases by 60%60\%60%, find width's percentage change if: (a) perimeter stays the same. (b) area stays the same.

Problem 330

Calcula cuántos rollos de material necesita comprar para insonorizar 4 paredes de 2 m x 2.2 m, considerando una puerta de 0.8 m.

Problem 331

Calcula el volumen de un archivador de 150 cm150 \mathrm{~cm}150 cm alto, 55 cm55 \mathrm{~cm}55 cm ancho y 60 cm60 \mathrm{~cm}60 cm fondo en m³.

Problem 332

Find the radius of a sphere with volume 4.5 m34.5 \mathrm{~m}^{3}4.5 m3 using the formula V=43πr3V=\frac{4}{3} \pi r^{3}V=34​πr3.

Problem 333

Find the length LLL and width WWW (with W≤LW \leq LW≤L) of a rectangle with perimeter 28 that maximizes area. What is the max area?

Problem 334

Calculate the area of quadrilateral ABCDABCDABCD with vertices A(0,2)A(0,2)A(0,2), B(4,7)B(4,7)B(4,7), C(8,2)C(8,2)C(8,2), D(4,3)D(4,3)D(4,3).

Problem 335

Calculate the area of a parallelogram with base 6 inches and height 3 inches. Use the formula: Area = base × height = 6×36 \times 36×3.

Problem 336

Find the area of a sector with radius 2 cm and central angle 90°, where OE = OF.

Problem 337

Yair added sawdust to a toilet. The seat is 0.4 m0.4 \mathrm{~m}0.4 m above ground and the pit bottom is 1.5 m1.5 \mathrm{~m}1.5 m below. 1. Find the distance from the toilet seat to the pit bottom in m\mathrm{m}m.2. Calculate the height change of the sawdust from the seat to the pit bottom.

Problem 338

Find the distance between Natasha's beagle at 254\frac{25}{4}425​ meters and her labrador at 5120\frac{51}{20}2051​ meters.

Problem 339

A tank is 4.5 m long, 3.5 m wide, and 2.8 m deep. Water is pumped at 6500 L/h. After 3 hours, what is the water level from the top?

Problem 340

What is the total cost of a rectangular plot measuring 1200 m×900 m1200 \mathrm{~m} \times 900 \mathrm{~m}1200 m×900 m if 1 hectare costs R5 200,00?

Problem 341

Find the length of a side of square ABCD if its area is 89 cm². What is xundefined\widehat{x}x?

Problem 342

Calculate the volume of a hole measuring 11.0 m×14.5 m×4.0 m11.0 \mathrm{~m} \times 14.5 \mathrm{~m} \times 4.0 \mathrm{~m}11.0 m×14.5 m×4.0 m and a truck bed 4 m×3 m×2.0 m4 \mathrm{~m} \times 3 \mathrm{~m} \times 2.0 \mathrm{~m}4 m×3 m×2.0 m. How many trips needed?

Problem 343

Find the area of the tiled walkway around a 24ft×12ft24 \mathrm{ft} \times 12 \mathrm{ft}24ft×12ft pool with a 2ft2 \mathrm{ft}2ft wide border.

Find the area of the region bound by the following equations: $y=6 x+6, \quad y=0, \quad x=3 \text { and } x=7$

Determine the area of the given square. $A=B * H$

$\text{Given a triangle with side lengths: } a = 12 \, \text{m}, \, b = 7.5 \, \text{m}, \, c = 8 \, \text{m}.$ \text{Find the perimeter and area of this triangle.}

A school playground is in the shape of a rectangle 400 feet long and 200 feet wide. If fencing costs $\$ 19$ per yard, what will it cost to place fencing around the playground? \\square$

4) A person throws a ball with an initial velocity of 15 meters $/ \mathrm{sec}$ at an angle of $20^{\circ}$ above the grd How far from the person will the ball land? Horizo

Area involving rectangles and triangles
A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer. $\square$

21. You have a 1200 -foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area and the dimensions of this largest rectangular enclosure? \begin{tabular}{|l|l|} \hline $\square$ \\ $\square$ \end{tabular}

A rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. $V=$ $\square$ (Simplify your answer. Do not factor.)

Line $\ell$ has equation $y=x-2$ . Find the distance between $\ell$ and the point $R(-5,0)$ . Round your answer to the nearest tenth.

A blueprint is drawn using a scale of $\frac{2 \mathrm{inm}}{25 \mathrm{ft}}$ . What length is represented by 1 mm ?
50 ft 12.5 ft 10.5 ft
23 ft

A blueprint is drawn using a scale of $\frac{2 \mathrm{inm}}{25 \mathrm{ft}}$ . What length is represented by 1 mm ?
50 ft 12.5 ft 10.5 ft
23 ft

A fish tank is in the shape of a cube. The volume of the tank is 64 cubic feet. What is the width, in inches, of one side of the fish tank?
192 inches 48 inches 96 inches 256 inches

Find the area of the figure. (Sides meet at right angles.) $\square$ $y d^{2}$ Gheck O 2024 McGraw Hill LLC. Al

Find the area of this parallelogram. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. $\square$ in

The ratio of the side length of a square to the square's perimeter is always 1 to 4 . Peter drew a square with a perimeter of 28 inches.
What is the side length of the square Peter drew?

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. What are the dimensions of her scale drawing using $3 \mathrm{~cm}$ for every $4 \mathrm{ft}$ ?

A $12.875-\mathrm{m}$ fence is one side of a rectangle. With $45.625 \mathrm{~m}$ left for the other sides, find the longer dimension.

Find the area of parallelogram $ABCD$ with sides 6 and 4 units and an angle of 125 degrees. Compare it to 24.

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. With a scale of $3 \mathrm{cm}$ for $4 \mathrm{ft}$ , find the drawing's dimensions.

A scale drawing shows a closet measuring $4.4 \mathrm{~cm}$ by $3.2 \mathrm{~cm}$ . With a scale of $2 \mathrm{~cm}$ to $1 \mathrm{~m}$ , find the actual area.

A rectangle has dimensions $10 \mathrm{~cm}$ by $8 \mathrm{~cm}$ . If length increases by $60\%$ , find width's percentage change if: (a) perimeter stays the same. (b) area stays the same.

Calcula el volumen de un archivador de $150 \mathrm{~cm}$ alto, $55 \mathrm{~cm}$ ancho y $60 \mathrm{~cm}$ fondo en m³.

Find the radius of a sphere with volume $4.5 \mathrm{~m}^{3}$ using the formula $V=\frac{4}{3} \pi r^{3}$ .

Find the length $L$ and width $W$ (with $W \leq L$ ) of a rectangle with perimeter 28 that maximizes area. What is the max area?

Calculate the area of quadrilateral $ABCD$ with vertices $A(0,2)$ , $B(4,7)$ , $C(8,2)$ , $D(4,3)$ .

Calculate the area of a parallelogram with base 6 inches and height 3 inches. Use the formula: Area = base × height = $6 \times 3$ .

Yair added sawdust to a toilet. The seat is $0.4 \mathrm{~m}$ above ground and the pit bottom is $1.5 \mathrm{~m}$ below.
1. Find the distance from the toilet seat to the pit bottom in $\mathrm{m}$ .
2. Calculate the height change of the sawdust from the seat to the pit bottom.

Find the distance between Natasha's beagle at $\frac{25}{4}$ meters and her labrador at $\frac{51}{20}$ meters.

What is the total cost of a rectangular plot measuring $1200 \mathrm{~m} \times 900 \mathrm{~m}$ if 1 hectare costs R5 200,00?

Find the length of a side of square ABCD if its area is 89 cm². What is $\widehat{x}$ ?

Calculate the volume of a hole measuring $11.0 \mathrm{~m} \times 14.5 \mathrm{~m} \times 4.0 \mathrm{~m}$ and a truck bed $4 \mathrm{~m} \times 3 \mathrm{~m} \times 2.0 \mathrm{~m}$ . How many trips needed?

Find the area of the tiled walkway around a $24 \mathrm{ft} \times 12 \mathrm{ft}$ pool with a $2 \mathrm{ft}$ wide border.

Find the map length of a road that is $3 \mathrm{~km}$ long, with a scale of $1: 120000$ . Answer in $\mathrm{cm}$ .

Find the range of the actual area of a rectangle with width $3.0 \mathrm{~cm}$ and length $8.0 \mathrm{~cm}$ .

Find the maximum absolute error for the measurements of an 8-sided polygon with given sides: $GF = 4cm$ , $FE = 3cm$ , $DC = 6cm$ , $CB = 8cm$ .

In an 8-sided polygon $ABCDEFGH$ with rectangles $ABCD$ and $EFGH$ , find:
(a) max error in cm. (b) min area of rectangle $ABCD$ . (c) min area of rectangle $EFGH$ . (d) range of actual area $x$ in cm².

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length $s$ .

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

Find the length of the latus rectum and the parabolic arc for the parabola given by $x^{2}=4 a y$ .

Find the length and width of a rectangular garden with area $96 \mathrm{~m}^{2}$ and perimeter $40 \mathrm{~m}$ .

Find the equation of line $O A$ , show $A$ is $(16,-8)$ , and calculate area of trapezium $O A B C$ .

Find the maximum load $P$ for an 8m beam with I section dimensions and stress limit of 340 MPa.

Find the volume of a donut box with length 9 in, width 4 in, and height 3 in: $V = l \times w \times h$ .

Find the volume of a donut box with dimensions: length = 9 in, width = 4 in, height = 3 in. Use $V = l \times w \times h$ .

Penelope's Pizzeria has a pizza box volume of 12 cubic units. Which dimensions are possible? A. $1 \times 12 \times 1$ B. $3 \times 2 \times 2$ C. $6 \times 3 \times 1$

Astiton wants to buy the box of peanuts with the most volume. Compare Box 1 ( $14 \times 7$ ) and Box 2 ( $105$ ). Which is larger?

Ashton needs to choose between two peanut boxes. Box \#1 has a volume of $14 \times 7 = 98$ cubic inches. Box \#2 is 105 cubic inches. Which box is larger?

Locate points of rectangle $ABCD$ at $A(2,2), B(2,-1), C(-1,-1), D(-1,2)$ , then find its perimeter and area.

Find the perimeter of a pentagon with sides 14, 12, 10, 8, and 6 inches using the expression $P = 14 + 12 + 10 + 8 + 6$ .

Punctele coliniare $A, B$ și $C$ au $B C=2 A C$ . Dacă $M$ și $N$ sunt mijloacele segmentelor $A C$ și $C B$ cu $M N=9 \mathrm{~cm}$ , găsește lungimea lui $A C$ : a) $3 \mathrm{~cm}$ ; b) $6 \mathrm{~cm}$ ; c) $18 \mathrm{~cm}$ .

Hitung luas bilik dalam $\mathrm{cm}^{2}$ jika 250 jubin berukuran $6.096 \times 10^{2} \mathrm{~mm}$ dan $3.048 \times 10^{2} \mathrm{~mm}$ .

Find a formula for the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

Find the volume of a right cone with a base diameter of $9.5 \mathrm{~cm}$ and a height of $16 \mathrm{~cm}$ .

The office floor plan is at a scale of $1:20$ . Find the actual length for $96 \mathrm{~cm}$ and pantry area in $\mathrm{cm}^{2}$ for $4.8 \mathrm{~m}^{2}$ .

In square $ABCD$ , area equals the sum of areas of triangles $ABE$ and $DCE$ . If $AB=6$ , find $CE$ . (a) 5 (b) 6 (c) 2 (d) 3 (e) 4

In square $ABCD$ with $AB=6$ , the area equals the sum of triangles $ABE$ and $DCE$ . Find length of $CE$ .

Find the area $x$ of hexagon $ABCDEF$ with rectangle $ABCD$ where $AB=9$ cm, $BC=16$ cm, $AE=8$ cm, and $FG=3$ cm.