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

C-75 Third Option

Explanation:

Answer 2

1.

EF is the median of the trapezoid ABCD, thus


`|EF|= (|AB|+|DC|)/(2)= (20+8)/(2)=14` units.

2.

The median EF bisects the altitude into 2 segments of equal length 6 units.

Thus the height of trapezoid EFCD is 6, and its 2 bases have length 14 and 8 units.

3.

From the area of the trapezoid formula:


`A_E_F_C_D=Height* (Base_1+Base_2)/(2)=6* (14+8)/(2)=6* (22)/(2)=66` (square units)


Answer: 66 square units