Math / Geometry

QuestionJoe 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. $f t$ .

Studdy Solution

STEP 1

What is this asking? We need to find the perimeter and area of the side of Joe's barn, which is shaped like a rectangle with a triangle on top! Watch out! Don't forget to add all the sides for the perimeter and remember the formulas for the area of a rectangle and a triangle.

STEP 2

1. Calculate the perimeter
2. Calculate the area of the rectangle
3. Calculate the area of the triangle
4. Calculate the total area

STEP 3

Alright, let's start with the perimeter!
The perimeter is the total distance around the outside of the barn's side.

STEP 4

We have two sides of the rectangle that are $11$ ft tall, and two triangle sides that are $7.43$ ft long each.
We don't need the $11$ ft base of the triangle, since it's inside the shape.

STEP 5

So, the total perimeter is $2 \cdot 11 + 2 \cdot 7.43$ .

STEP 6

$2 \cdot 11 + 2 \cdot 7.43 = 22 + 14.86 = 36.86$

STEP 7

The perimeter is $36.86$ ft!

STEP 8

Now, let's move on to the area!
We'll start with the rectangle.

STEP 9

The area of a rectangle is length times width.
Here, both the length and width are $11$ ft.

STEP 10

So, the area of the rectangle is $11 \cdot 11$ .

STEP 11

$11 \cdot 11 = 121$

STEP 12

The area of the rectangle is $121$ sq. ft.

STEP 13

Next, the area of the triangle!

STEP 14

The area of a triangle is one-half base times height.
The base is $11$ ft and the height is $5$ ft.

STEP 15

So, the area of the triangle is $\frac{1}{2} \cdot 11 \cdot 5$ .

STEP 16

$\frac{1}{2} \cdot 11 \cdot 5 = \frac{1}{2} \cdot 55 = 27.5$

STEP 17

The area of the triangle is $27.5$ sq. ft.

STEP 18

Finally, let's put it all together!

STEP 19

The total area of the barn's side is the area of the rectangle plus the area of the triangle.

STEP 20

So, the total area is $121 + 27.5$ .

STEP 21

$121 + 27.5 = 148.5$

STEP 22

The total area is $148.5$ sq. ft!

STEP 23

The perimeter of the side of the barn is $36.86$ ft.
The area of the side of the barn is $148.5$ sq. ft.

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Studdy Solution

STEP 1

What is this asking? We need to find the perimeter and area of the side of Joe's barn, which is shaped like a rectangle with a triangle on top! Watch out! Don't forget to add all the sides for the perimeter and remember the formulas for the area of a rectangle and a triangle.

STEP 2

1. Calculate the perimeter2. Calculate the area of the rectangle3. Calculate the area of the triangle4. Calculate the total area

STEP 3

Alright, let's **start** with the perimeter!The perimeter is the total distance around the outside of the barn's side.

STEP 4

We have two sides of the rectangle that are 111111 ft tall, and two triangle sides that are 7.437.437.43 ft long each.We don't need the 111111 ft base of the triangle, since it's inside the shape.

STEP 5

So, the **total perimeter** is 2⋅11+2⋅7.432 \cdot 11 + 2 \cdot 7.432⋅11+2⋅7.43.

STEP 6

2⋅11+2⋅7.43=22+14.86=36.862 \cdot 11 + 2 \cdot 7.43 = 22 + 14.86 = 36.862⋅11+2⋅7.43=22+14.86=36.86

STEP 7

The **perimeter** is 36.8636.8636.86 ft!

STEP 8

Now, let's **move on** to the area!We'll **start** with the rectangle.

STEP 9

The **area of a rectangle** is length times width.Here, both the length and width are 111111 ft.

STEP 10

So, the **area of the rectangle** is 11⋅1111 \cdot 1111⋅11.

STEP 11

11⋅11=12111 \cdot 11 = 12111⋅11=121

STEP 12

The **area of the rectangle** is 121121121 sq. ft.

STEP 13

Next, the **area of the triangle**!

STEP 14

The **area of a triangle** is one-half base times height.The base is 111111 ft and the height is 555 ft.

STEP 15

So, the **area of the triangle** is 12⋅11⋅5\frac{1}{2} \cdot 11 \cdot 521​⋅11⋅5.

STEP 16

12⋅11⋅5=12⋅55=27.5\frac{1}{2} \cdot 11 \cdot 5 = \frac{1}{2} \cdot 55 = 27.521​⋅11⋅5=21​⋅55=27.5

STEP 17

The **area of the triangle** is 27.527.527.5 sq. ft.

STEP 18

Finally, let's **put it all together**!

STEP 19

The **total area** of the barn's side is the area of the rectangle plus the area of the triangle.

STEP 20

So, the **total area** is 121+27.5121 + 27.5121+27.5.

STEP 21

121+27.5=148.5121 + 27.5 = 148.5121+27.5=148.5

STEP 22

The **total area** is 148.5148.5148.5 sq. ft!

STEP 23

The perimeter of the side of the barn is 36.8636.8636.86 ft.The area of the side of the barn is 148.5148.5148.5 sq. ft.

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1. Calculate the perimeter
2. Calculate the area of the rectangle
3. Calculate the area of the triangle
4. Calculate the total area

Alright, let's start with the perimeter!
The perimeter is the total distance around the outside of the barn's side.

We have two sides of the rectangle that are $11$ ft tall, and two triangle sides that are $7.43$ ft long each.
We don't need the $11$ ft base of the triangle, since it's inside the shape.

So, the total perimeter is $2 \cdot 11 + 2 \cdot 7.43$ .

$2 \cdot 11 + 2 \cdot 7.43 = 22 + 14.86 = 36.86$

The perimeter is $36.86$ ft!

Now, let's move on to the area!
We'll start with the rectangle.

The area of a rectangle is length times width.
Here, both the length and width are $11$ ft.

So, the area of the rectangle is $11 \cdot 11$ .

$11 \cdot 11 = 121$

The area of the rectangle is $121$ sq. ft.

Next, the area of the triangle!

The area of a triangle is one-half base times height.
The base is $11$ ft and the height is $5$ ft.

So, the area of the triangle is $\frac{1}{2} \cdot 11 \cdot 5$ .

$\frac{1}{2} \cdot 11 \cdot 5 = \frac{1}{2} \cdot 55 = 27.5$

The area of the triangle is $27.5$ sq. ft.

Finally, let's put it all together!

The total area of the barn's side is the area of the rectangle plus the area of the triangle.

So, the total area is $121 + 27.5$ .

$121 + 27.5 = 148.5$

The total area is $148.5$ sq. ft!

The perimeter of the side of the barn is $36.86$ ft.
The area of the side of the barn is $148.5$ sq. ft.