Use the image to answer the question.
An illustration shows a net diagram. The center of the diagram is a triangle. Each side of this triangle forms the base of one of three other triangles extending outward from the center triangle. One side of the center triangle measures 10 meters. The perpendicular height of the center triangle measures 8.7 meters. The perpendicular height of the triangle attached to the left of the center triangle measures 14 meters.
Find the lateral surface area of the triangular pyramid with an equilateral base represented in the net.
(1 point)
m2
The lateral surface area of a triangular pyramid can be found using the formula:
Lateral surface area = 1/2 * perimeter of base * slant height
First, we need to find the perimeter of the base, which is an equilateral triangle. Since one side of the center triangle is 10 meters, the sides of the equilateral triangle are also 10 meters each.
Perimeter of the base = 3 * 10 = 30 meters
Next, we need to find the slant height of the pyramid. The slant height is the height of the attached triangle, which is 14 meters.
Now, we can calculate the lateral surface area:
Lateral surface area = 1/2 * 30 * 14 = 210 square meters
Therefore, the lateral surface area of the triangular pyramid is 210 square meters.