Question

The area of a trapezoid is $80$. The length of one base is $4$ units greater than the other base, and the height of the trapezoid is $12$. Find the length of the median of the trapezoid.

Answer 1

Let the length of the shorter base be $x$, so the length of the longer base is $x+4$. The area of the trapezoid is $\frac{1}{2}(x+x+4)(12)=80$, which simplifies to $12(2x+4)=240$. Solving for $x$, we find $x=8$. The length of the median is the average of the lengths of the two bases, or $\frac{8+12}{2}=\boxed{10}$ units.