Question

Find the area of a trapezoid with base lengths (x + 3) and (x + 1) and height (2x - 6).

Answer 1

`\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=2x-6\\ a=x+3\\ b=x+1 \end{cases}\implies A=\cfrac{(2x-6)[(x+3)+(x+1)]}{2} \\\\\\ A=\cfrac{(2x-6)[2x+4]}{2}\implies A=\cfrac{(2x-6)2(x+2)}{2}\implies A=(2x-6)(x+2) \\\\\\ A=2x^2+6x+4x+12\implies A=2x^2+10x+12`