Math / Geometry

QuestionA 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. $\square$
m $m^{2}$ $\mathrm{m}^{3}$

Studdy Solution

STEP 1

1. The rectangle has dimensions $10 \, \text{m}$ by $7 \, \text{m}$ .
2. The right triangle removed has legs measuring $6 \, \text{m}$ and $8 \, \text{m}$ .
3. The area of the shaded region is the area of the rectangle minus the area of the triangle.

STEP 2

1. Calculate the area of the rectangle.
2. Calculate the area of the right triangle.
3. Subtract the area of the triangle from the area of the rectangle to find the area of the shaded region.

STEP 3

Calculate the area of the rectangle using the formula:
$\text{Area of Rectangle} = \text{Length} \times \text{Width}$
Substitute the given values:
$\text{Area of Rectangle} = 10 \, \text{m} \times 7 \, \text{m}$
$= 70 \, \text{m}^2$

STEP 4

Calculate the area of the right triangle using the formula:
$\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$
Substitute the given values:
$\text{Area of Triangle} = \frac{1}{2} \times 6 \, \text{m} \times 8 \, \text{m}$
$= \frac{1}{2} \times 48 \, \text{m}^2$
$= 24 \, \text{m}^2$

STEP 5

Subtract the area of the triangle from the area of the rectangle to find the area of the shaded region:
$\text{Area of Shaded Region} = \text{Area of Rectangle} - \text{Area of Triangle}$
$= 70 \, \text{m}^2 - 24 \, \text{m}^2$
$= 46 \, \text{m}^2$
The area of the shaded region is:
$\boxed{46 \, \text{m}^2}$

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