Question

The figure below is a net for a square pyramid. What is the surface area of the square pyramid, in square inches?

Answer 1

First, we can easily find the area of the base since it has a square shape:

$\begin{gathered} A_b=3.2\cdot3.2=10.24 \\ \Rightarrow A_b=10.24in^2 \end{gathered}$

now, notice that each side is a triangle with the following measures:

then, the area of a single side is:

$\begin{gathered} A_s=\frac{3.2\cdot3.3}{2}=\frac{10.56}{2}=5.28 \\ \Rightarrow A_s=5.28in^2 \end{gathered}$

since the pyramid has 4 triangular sides and one base, adding all the areas together we get:

$\begin{gathered} A=A_b+4\cdot A_s=10.24in^2+4\cdot(5.28in^2)=10.24in^2+51.12in^2=31.36in^2 \\ \Rightarrow A=31.36in^2 \end{gathered}$

therefore, the surface area of the square pyramid is 31.36in^2