Question

find the surface area of the square pyramid (above) using its net (below).

Explanation:

Step1: Calculate base area

The base is a square with side - length $s = 2$. The area of a square is $A_{base}=s^2$. So, $A_{base}=2^2 = 4$.

Step2: Calculate area of one triangular face

The base of each triangular face is $b = 2$ and the height is $h = 2$. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$. So, $A_{triangle}=\frac{1}{2}\times2\times2=2$.

Step3: Calculate total area of triangular faces

There are 4 triangular faces. So the total area of the triangular faces is $A_{triangles}=4\times A_{triangle}=4\times2 = 8$.

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. So, $A=A_{base}+A_{triangles}=4 + 8=12$.

Answer:

12