Question

What is the surface area of the square pyramid represented bythe net?9 m6 mEnter your answer in the box6 m9 m9 mma9 m

Answer 1

The surface area of the square pyramid consists of the area of four identical triangles and the square base. The formulas to obtain the area of each one of those two kinds of figures are

`\begin{gathered} A_{\text{square}}=l^2 \\ A_{\text{triangle}}=(1)/(2)bh \end{gathered}`

In our case,

`l=b=6,h=9`

Thus, the surface area is

`\begin{gathered} A_{\text{surface}}=A_{\text{square}}+4A_{\text{triangle}} \\ \Rightarrow A_{\text{surface}}=6^2+4((1)/(2)6\cdot9)=36+2\cdot54=36+108=144 \\ \Rightarrow A_{\text{surface}}=144 \end{gathered}`

Thus, the answer is 144m^2