Question

A trapezoid has an area of 66 square miles. One base is 8 miles long. The height measures 12 miles. What is the length of the other base?

Answer 1

Check the picture below.

`\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=8\\ h=12\\ A=66 \end{cases}\implies 66=\cfrac{12(8+b)}{2} \\\\\\ 66=6(8+b)\implies \cfrac{66}{6}=8+b\implies 11=8+b\implies 3=b`