Question

find the surface area of the square pyramid shown below. units²

Explanation:

Step1: Calculate base area

The base is a square with side - length $s = 8$. The area of the base $A_{base}=s^2$. So, $A_{base}=8^2 = 64$.

Step2: Calculate area of one triangular face

The area of a triangle is $A_{\triangle}=\frac{1}{2}\times base\times height$. Here, the base of each triangular face is the side - length of the square base ($b = 8$) and the height of each triangular face (slant height) $h = 6$. So, $A_{\triangle}=\frac{1}{2}\times8\times6=24$.

Step3: Calculate total area of triangular faces

A square pyramid has 4 triangular faces. The total area of the 4 triangular faces $A_{triangles}=4\times A_{\triangle}$. So, $A_{triangles}=4\times24 = 96$.

Step4: Calculate surface area

The surface area $A$ of the square pyramid is the sum of the base area and the total area of the triangular faces. $A=A_{base}+A_{triangles}$. So, $A = 64+96=160$.

Answer:

160