Question

Dave had a section of his roof damaged by hail, so he needs to replace the shingles. The roof section can be represented by trapezoid JKLM. How many square feet of shingles must he order?
A.
272 ft^2
B.
283.2 ft^2
C.
352 ft^2
D.
459 ft^2

Answer 1

The problem is looking for the area of the trapezoid. To solve for the area of a trapezoid, we can cut them into different shapes like rectangle and triangles.

First, we draw altitudes at M and L to make a rectangle with length 22 ft and width 17 ft. We subtract 22 ft from 32 ft and divide it by 2 in order to get the base for each triangle.
(32-22)/2 = 5 ft.

Next, we find the area of the rectangle. A = LW = 22 ft x 17 ft = 374 ft^2.

Then we find the area of the triangle: A = 0.5BH = 0.5 x 5 ft x 17 ft = 42.5 ft^2

Total area = 374 ft^2 + 2(42.5 ft^2) = 459 ft^2.
The answer is D.