Question

find the surface area of a square pyramid with side length 6 ft and slant height 5 ft.

Explanation:

Step1: Calculate base area

The base is a square with side - length $a = 6$ ft. The area of the base $B=a^{2}$. So $B = 6^{2}=36$ square feet.

Step2: Calculate area of one triangular face

The area of a triangle is $A_{\triangle}=\frac{1}{2}bh$, where the base $b$ of each triangular face is the side - length of the square base ($b = 6$ ft) and the height is the slant height $l = 5$ ft. So $A_{\triangle}=\frac{1}{2}\times6\times5 = 15$ square feet.

Step3: Calculate total area of triangular faces

A square pyramid has 4 triangular faces. The total area of the 4 triangular faces $A_{triangles}=4\times A_{\triangle}$. So $A_{triangles}=4\times15 = 60$ square feet.

Step4: Calculate surface area

The surface area $SA$ of a square pyramid is the sum of the base area and the total area of the triangular faces. So $SA=B + A_{triangles}=36+60 = 96$ square feet.

Answer:

96 square feet