Find the lateral surface area of the triangular pyramid with an equilateral base represented in the net

Question

10 m
8.7 m
14 m

Answer 1

To find the lateral surface area of a triangular pyramid with an equilateral base, we need to first determine the slant height of the pyramid.

Given:
Base side length = 10 m
Height from base center to apex = 8.7 m
Side slant height of pyramid = 14 m

The lateral surface area can be calculated using the formula:

Lateral Surface Area = 1/2 * Perimeter of base * Slant height

Since the base is an equilateral triangle, the perimeter of the base can be calculated as:
Perimeter = 3 * Base side length
Perimeter = 3 * 10m
Perimeter = 30m

Now we can substitute the values into the formula to find the lateral surface area:
Lateral Surface Area = 1/2 * 30m * 14m
Lateral Surface Area = 210 m^2

Therefore, the lateral surface area of the triangular pyramid is 210 square meters.