Question

30 ft

10 ft
8 ft
16 ft

Find the base of a triangle with the same area as the shaded region. The height of the triangle is 25 feet. Show ALL work.
(Hint
Area of a rectangle = Length× Width
Area of a triangle = 1/2× Base× Height)​

Answer 1

32 ft

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

Answer 2

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.

`A_ {sr} = 30 * 16-10 * 8\\A_ {sr} = 480-80\\A_ {sr} = 400`

Thus, the area of the shaded region is
`400 \ ft ^ 2`

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

`400 = \frac {1} {2} b * 25\\400 = 12.5b`

Dividing between 12.5 on both sides of the equation:

`b = 32`

Thus, the base of the triangle is 32.

Answer:

32