Question

What’s the area of the figure?

Answer 1

we can pretty much split the middle part into two trapezoids. Check the picture below.

so we really have one trapezoid and one square, each twice, so simply let's get the area of the trapezoid and sum it up with the area of the square, twice, and that's the area of the shape.

`\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{\textit{parallel sides}}{bases}\\[-0.5em] \hrulefill\\ h=5\\ a=3\\ b=7 \end{cases}\implies A=\cfrac{5(3+7)}{2}\implies A=25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{sum of areas}}{[25+(3\cdot 3)]}\cdot \stackrel{twice}{2}\implies [34]2\implies \underset{in^2}{68}`