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 is given by the formula:
Lateral Surface Area = 0.5 * Perimeter of Base * Slant Height
Since the base of the triangular pyramid is equilateral, each side of the base triangle is 10 meters. The perimeter of the base triangle is therefore 3 * 10 = 30 meters.
The slant height of the triangular pyramid is the height of the attached triangle, which is 14 meters.
Plugging these values into the formula:
Lateral Surface Area = 0.5 * 30 * 14 = 210 square meters
Therefore, the lateral surface area of the triangular pyramid is 210 square meters.