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
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The lateral surface area of a triangular pyramid with an equilateral base can be calculated using the formula:
Lateral Surface Area = 1/2 * perimeter of base * slant height
In this case, the perimeter of the base (equilateral triangle) can be calculated as 3 times the length of one side of the base. The slant height is the height of the attached triangle, which is 14 meters.
Since one side of the center triangle is given as 10 meters, the perimeter of the equilateral triangle is 3 * 10 = 30 meters.
Therefore, the lateral surface area of the triangular pyramid is:
Lateral Surface Area = 1/2 * 30 * 14 = 210 square meters
So, the lateral surface area of the triangular pyramid in the net diagram is 210 square meters.