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 please.
(1 point)
m2
To find the lateral surface area of the triangular pyramid, we need to find the area of each of the four triangles and add them up.
First, let's find the area of the base triangle (which is equilateral). Since the length of one side is 10 meters, and it is an equilateral triangle, we can use the formula for the area of an equilateral triangle:
Area = sqrt(3) / 4 * side^2
Area = sqrt(3) / 4 * 10^2
Area = sqrt(3) / 4 * 100
Area = 25sqrt(3) m^2
Next, let's find the area of the lateral faces of the pyramid. Since all the lateral faces are triangles with the same height (8.7 meters) and different base sides, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
For the lateral face attached to the left of the center triangle, the base is 10 meters and the height is 8.7 meters:
Area = 1/2 * 10 * 8.7
Area = 43.5 m^2
Since there are three identical lateral faces in the pyramid, the total area of the lateral faces is:
Total lateral surface area = 3 * 43.5 m^2
Total lateral surface area = 130.5 m^2
Therefore, the lateral surface area of the triangular pyramid is 130.5 square meters.