To find the lateral surface area of a pyramid with a base that is an equilateral triangle, we need to follow a series of steps:
1. Determine the perimeter of the base:
Since the base is an equilateral triangle, all three sides are of equal length. If the length of each side of the triangular base is given as 5 inches, then the perimeter of the base can be calculated using the formula for the perimeter of an equilateral triangle:
[tex]\[
\text{Perimeter} = 3 \times \text{side length} = 3 \times 5 = 15 \text{ inches}
\][/tex]
2. Use the formula for the lateral surface area:
The formula for the lateral surface area (LSA) of a pyramid is:
[tex]\[
\text{Lateral Surface Area} = \frac{\text{Perimeter of base} \times \text{Slant Height}}{2}
\][/tex]
Here, the slant height is given as 12 inches.
3. Substitute the known values into the formula:
Now, we will substitute the perimeter of the base and the slant height into the formula:
[tex]\[
\text{Lateral Surface Area} = \frac{15 \times 12}{2}
\][/tex]
4. Compute the result:
Perform the multiplication and division to find the lateral surface area:
[tex]\[
\text{Lateral Surface Area} = \frac{15 \times 12}{2} = \frac{180}{2} = 90 \text{ square inches}
\][/tex]
Hence, the lateral surface area of the pyramid is 90 square inches.
