Question

1. find the surface area of the square pyramid.

Explanation:

Step1: Find base - area

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

Step2: Find the area of one triangular face

The formula for the area of a triangle is \(A_{\triangle}=\frac{1}{2}bh\). Here, the base of the triangle \(b = 4\) ft and the height of the triangle \(h = 6\) ft. So \(A_{\triangle}=\frac{1}{2}\times4\times6 = 12\) square - feet.

Step3: Find the total area of the four triangular faces

Since there are 4 triangular faces, \(A_{triangles}=4\times A_{\triangle}=4\times12 = 48\) square - feet.

Step4: Find the surface area of the square pyramid

The surface area \(A\) of a square pyramid is the sum of the base - area and the area of the four triangular faces. So \(A=A_{base}+A_{triangles}=16 + 48=64\) square - feet.

Answer:

64 square feet