SOLUTION: Find the volume, to the nearest tenth, of a pyramid that is 6 feet tall and whose base is an equilateral triangle with sides each 10 feet long.

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Question 551333: Find the volume, to the nearest tenth, of a pyramid that is 6 feet tall and whose base is an equilateral triangle with sides each 10 feet long.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
For a pyramid, the volume is:
V+=+B%2Ah where: B = area of the base and h = the height of the pyramid.
Use Hero's formula to find the area of the triangular base:
A+=+sqrt%28S%28S-a%29%28S-b%29%28S-c%29%29 where S = semi perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.
A+=+sqrt%2815%2815-10%29%2815-10%29%2815-10%29%29
A+=+sqrt%2815%28125%29%29
A+=+sqrt%281875%29
A+=+43.3
V+=+43.3%286%29
V+=+259.8cu.ft.