Question

find the surface area of a square pyramid with side length 4 ft and slant height 3 ft.
answer attempt 1 out of 1
ft² submit answer

Explanation:

Step1: Calculate the area of the base

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

$$A_{base}=4^{2}=16$$

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A_{\triangle}=\frac{1}{2}\times base\times height\). Here, the base of the triangular face is \(b = 4\) ft (side - length of the square base) and the height (slant height) \(l = 3\) ft.

$$A_{\triangle}=\frac{1}{2}\times4\times3 = 6$$

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) triangular faces, \(A_{triangles}=4\times A_{\triangle}\)

$$A_{triangles}=4\times6=24$$

Step4: Calculate the total surface area

The total surface area \(A\) of the square pyramid is the sum of the area of the base and the area of the four triangular faces. \(A = A_{base}+A_{triangles}\)

$$A=16 + 24$$

Answer:

\(40\)