Question

what is the surface area of the square pyramid?
6 sq ft
16 sq ft
24 sq ft

Explanation:

Step1: Calculate base - area

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

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A_{\triangle}=\frac{1}{2}bh$, where the base $b = 2$ ft and the height $h = 3$ ft. So, $A_{\triangle}=\frac{1}{2}\times2\times3 = 3$ square feet.

Step3: Calculate total area of triangular faces

There are 4 triangular faces. So the total area of the triangular faces is $A_{triangles}=4\times A_{\triangle}=4\times3 = 12$ square feet.

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, $A=A_{base}+A_{triangles}=4 + 12=16$ square feet.

Answer:

16 sq ft