Question

find the lateral surface area of this pyramid whose base is an equilateral triangle. its slant height is 14 ft and the length of each side of the triangular base is 6 ft. lsa = ? ft²

Explanation:

Step1: Recall the formula for the lateral surface area (LSA) of a regular pyramid. The formula is \( LSA=\frac{1}{2} \times \text{Perimeter of base} \times \text{Slant height} \).

First, find the perimeter of the equilateral triangular base. Since each side of the equilateral triangle is 6 ft, and a triangle has 3 sides, the perimeter \( P = 3\times6=18 \) ft.

Step2: Substitute the values of perimeter and slant height into the formula.

The slant height \( l = 14 \) ft. So, \( LSA=\frac{1}{2} \times 18\times14 \).
First, calculate \( \frac{1}{2}\times18 = 9 \), then \( 9\times14 = 126 \).

Answer:

126