Question

In trapezoid ABCD, the parallel sides AB and CD have lengths of 8 and 20 units, respectively, and the altitude is 12 units. Points E and F are the midpoints of sides AD and BC, respectively. What is the area of quadrilateral EFCD in square units?

Answer 1

The length of side EF is the average of the lengths of the bases AB and CD of trapezoid ABCD.
EF = (8 + 20)/2 = 14
Trapezoid EF has bases 14 and 20.
The height of trapezoid EFCD is half the height of trapezoid ABCD, or 6.

A = (B + b)h/2 = (20 + 14) * 6 / 2 = 102

Answer: The area of trapezoid EFCD is 102 square units