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Difficult

Polygon Areas: Trapezoid

GMAT-UZVXPY

A given trapezoid $ABCD$ has a line segment $AE$ that is perpendicular to side $CD$. Segment $AE$ is $4$ inches and triangle $ACE$ has area $8$ square inches.

If segment $BE$ is $ 4\sqrt{2} $inches and side $CD$ is $12$ inches, what is the area of trapezoid $ABCD$?

A

$24$ square inches

B

$30$ square inches

C

$32$ square inches

D

$36$ square inches

E

$40$ square inches