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 $4$. The area of a square is $A_{base}=s^2$, so $A_{base}=4\times4 = 16$.

Step2: Calculate area of one triangular face

The triangular faces have base $b = 4$ and height $h = 3$. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$, so $A_{triangle}=\frac{1}{2}\times4\times3=6$.

Step3: Calculate total area of triangular faces

There are 4 triangular faces. The total area of the triangular faces is $A_{triangles}=4\times A_{triangle}=4\times6 = 24$.

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 $A=A_{base}+A_{triangles}=16 + 24=40$.

Answer:

40