Question

the top of a desk is shaped like the trapezoid shown, which has an area of 792 square inches. each triangular section has an area of 216 square inches. what is the height of the trapezoid? show your work.

Explanation:

Step1: Find area of two triangles

There are two triangular sections, each with area 216. So total area of triangles: \(2\times216 = 432\)

Step2: Find area of the parallelogram

Subtract triangle area from trapezoid area: \(792 - 432 = 360\)

Step3: Recall parallelogram area formula

Area of parallelogram is \(base\times height\). The base here is 20 in. Let height be \(h\). So \(20\times h = 360\)

Step4: Solve for height

\(h=\frac{360}{20}=18\)

Answer:

The height of the trapezoid is 18 inches.