Question

The area of a trapezoid is 864cm2. It has a height of 24 cm, and the length of one of its bases is 30 cm. What is the length of the other base?

Answer 1

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}\quad \begin{cases} a,b=\stackrel{bases}{\textit{parallel sides}}\\ h=height\\ ---------\\ A=864\\ h=24\\ a=30 \end{cases}\implies 864=\cfrac{24(30+b)}{2} \\\\\\ 864=12(30+b)\implies \cfrac{864}{12}=30+b\implies 72=30+b \\\\\\ 42=b$