An architect is designing a glass greenhouse in the form of a triangular pyramid for the botanical gardens. Find the surface area of the triangular pyramid with a base of 100 ft., a base height of 86.6 ft., and a slant height of 120 ft.
To find the surface area of the triangular pyramid, we need to find the area of each of the four triangular faces and add them together.
The formula to find the area of a triangle is 1/2 * base * height.
Using this formula, we can find the area of the base triangle:
Area = 1/2 * 100 ft * 86.6 ft
Area = 4330 square ft
Now, let's find the area of the other three triangles. Each of these triangles has the same height (120 ft) and slant height (120 ft).
Area = 1/2 * base * height
Area = 1/2 * 100 ft * 120 ft
Area = 6000 square ft
Now, we have the surface area of three triangles. Since the triangular pyramid has 4 equal faces, we need to multiply these values by 3.
Total surface area = 3 * (4330 square ft + 6000 square ft)
Total surface area = 3 * 10330 square ft
Total surface area = 30,990 square ft
Therefore, the surface area of the triangular pyramid is 30,990 square feet.