To find the lateral surface area (LSA) of a pyramid with a base that is an equilateral triangle, follow these steps:
1. Identify the given values:
- Slant height (l) of the pyramid: 14 feet
- Side length (a) of the equilateral triangle base: 6 feet
2. Determine the perimeter of the base:
- Since the base is an equilateral triangle, all three sides have the same length.
- Therefore, the perimeter of the base (P) is calculated as follows:
[tex]\[
P = 3 \times a
\][/tex]
Substituting the given side length:
[tex]\[
P = 3 \times 6 = 18 \text{ feet}
\][/tex]
3. Calculate the lateral surface area (LSA):
- The formula to find the lateral surface area of a pyramid is:
[tex]\[
\text{LSA} = \frac{P \times l}{2}
\][/tex]
Where [tex]\( P \)[/tex] is the perimeter of the base and [tex]\( l \)[/tex] is the slant height.
Substituting the values we have:
[tex]\[
\text{LSA} = \frac{18 \times 14}{2}
\][/tex]
4. Simplify the calculation:
[tex]\[
\text{LSA} = \frac{252}{2} = 126 \text{ square feet}
\][/tex]
Thus, the lateral surface area of the pyramid is [tex]\(126 \text{ ft}^2\)[/tex].
