Question

what is the surface area of the square pyramid? 6 sq ft 16 sq ft 24 sq ft 28 sq ft

Explanation:

Step1: Calculate the area of the square base

The formula for the area of a square is \(A = s^2\), where \(s\) is the side length. Here \(s = 2\) ft, so \(A_{base}=2^2=4\) sq ft.

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A=\frac{1}{2}bh\), where \(b\) is the base and \(h\) is the height. Here \(b = 2\) ft and \(h = 3\) ft, so \(A_{triangle}=\frac{1}{2}\times2\times3 = 3\) sq ft.

Step3: Calculate the total area of the four triangular faces

Since there are 4 triangular faces, \(A_{triangles}=4\times A_{triangle}=4\times3 = 12\) sq ft.

Step4: Calculate the total surface area of the square pyramid

The total surface area \(A = A_{base}+A_{triangles}\), so \(A=4 + 12=16\) sq ft.

Answer:

16 sq ft