Question

A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.

Answer 1

29 square ft.

Explanation:

To solve this problem you need to find the area of both shapes, let's start with the rectangle.

lw = A

3 * 7 = 21

The area of the rectangle is 21.

The formula for area of a triangle is 1/2bh.

1/2(10*10)

A = 50

Now we need to subtract to get the area of the shaded region.

50-21 = 29.

Therefore the area of the shaded region is 29.

Answer 2

Answer:
29.5 yd²
Explanation:
First we find the area of the triangle.
The base of the triangle is 5+4 = 9 yd.
The height of the triangle is 6+5 = 11 yd.
The formula for the area of a triangle is A = 1/2bh; this gives us
A = 1/2(9)(11) = 1/2(99) = 49.5 yd²
Next we find the area of the rectangle that is removed. The length of the rectangle is 4 and the width is 5. The area of a rectangle is given by
A = l*w; for our rectangle, we have
A = 4(5) = 20 yd²
The shaded region will have an area of
49.5 yd² - 20 yd² = 29.5 yd²