Question

Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 7.5 km. 9 km. 9 km. km² Surface Area:

Answer 1

We can split this prism into 5 planar figures: 1 square and 4 equal triangles. The area of the square is given by

$\begin{gathered} A_{\text{square}}=L^2 \\ A_{\text{square}}=9^2 \\ A_{\text{square}}=81km^2 \end{gathered}$

On the other hand, the area of one triangle is given by

$\begin{gathered} A_{\text{triangle}}=\frac{1}{2}\text{base}\times height \\ A_{\text{triangle}}=\frac{1}{2}9\times7.5 \\ A_{\text{triangle}}=33.75km^2 \end{gathered}$

Then, the surface area S is given by

$S=A_{\text{square}}+4\cdot A_{\text{triangle}}$

By substituting our last results, we have

$\begin{gathered} S=81+4\times33.75 \\ S=216km^2 \end{gathered}$

then, the answer is 216 square kilometers