Find the area of the quadrilateral in the trapezoid

Geometry Level 1

$ABCD$ is a trapezoid, where $AB||CD$ . Points $E$ and $F$ are the midpoints of $AD$ and $BC$ , respectively. The perpendicular distance from $AB$ to $CD$ is $12$ . Given that $AB=12$ and $DC=24$ , find the area of quadrilateral $ABFE$ .

The answer is 90.

1 solution

A Former Brilliant Member
Nov 7, 2017

The midline of a trapezoid is the line connecting the midpoints of the trapezoid’s sides. This line is parallel to the bases of the trapezoid and its length is equal to the halfsum of their lengths. So $EF=\dfrac{12+24}{2}=18$ . It follows that quadrilateral $ABFE$ is a trapezoid. So its height is $\dfrac{12}{2}=6$ . And the area is $\dfrac{1}{2}(12+18)(6)=90$ .

Find the area of the quadrilateral in the trapezoid

The answer is 90.

1 solution

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