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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To find the lateral surface area of the triangular pyramid, we first need to find the area of each of the four triangles in the net diagram.
For the center triangle:
Area = 0.5 * base * height
Area = 0.5 * 10 * 8.7
Area = 43.5 m²
For the three triangles attached to the center triangle:
Area = 0.5 * base * height
Area = 0.5 * 10 * 14
Area = 70 m² (for each of the three triangles)
Now, the lateral surface area of the triangular pyramid would be the sum of the surface areas of all four triangles.
Lateral Surface Area = 3 * 70 + 43.5
Lateral Surface Area = 210 + 43.5
Lateral Surface Area = 253.5 m²
Therefore, the lateral surface area of the triangular pyramid is 253.5 m².