30 ft10 ft8 ft16 ftfind the base of a triangle with the same area as the shaded region. the height of the triangle is 25 feet. show all work.(hintarea of a rectangle = length× widtharea of a triangle = 1/2× base× height)

32 ft

Step-by-step explanation:

find the area of the large rectangle:

30 x 16 = 480

find the area of the small rectangle:

10 x 8 = 80

subract the small rectangle from the big rectangle to get the area of the shaded region:

480 - 80 = 400

now plug this area and the height into the equation for triangle area:

A = bh/2

400 = b(25)/2 multiply both sides by 2

2(400) = 2(25b/2)

800 = 25b divide both sides by 25

800/25 = 25b/25

32 = b

For this case we have that the area of the shaded region is given by the subtraction of the large rectangle minus the small rectangle.

Thus, the area of the shaded region is

If the triangle must have the same area and a height of 25, then we have:

Dividing between 12.5 on both sides of the equation:

Thus, the base of the triangle is 32.

32

send it over

step-by-step explanation: