Question

1. find the surface area of the square pyramid.

Explanation:

Step1: Calculate base area

The base is a square with side length $4$ ft. The area of a square is $A_{base}=s^2$, so $A_{base}=4^2 = 16$ square - feet.

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, the base $b = 4$ ft and the height $h = 5$ ft. So $A_{triangle}=\frac{1}{2}\times4\times5=10$ square - feet.

Step3: Calculate total area of 4 triangular faces

Since there are 4 triangular faces, $A_{triangles}=4\times A_{triangle}=4\times10 = 40$ square - feet.

Step4: Calculate surface area

The surface area $A$ of a square - pyramid is the sum of the base area and the area of the 4 triangular faces. So $A=A_{base}+A_{triangles}=16 + 40=56$ square - feet.

Answer:

56 square feet