1953 AHSME Problems/Problem 13
Problem
A triangle and a trapezoid are equal in area. They also have the same altitude. If the base of the triangle is 18 inches, the median of the trapezoid is:
Solution
We know that the area of a trapezoid is where
is the median and the area of a triangle is
. We know that
and the height of the trapezoid is congruent to the height of the triangle. Thus, we get
, so
.