SOLUTION: Please help me 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 155041: Please help me 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(6098) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a regular pyramid is found by:
V+=+%281%2F3%29Bh where: B = area of the base and h = the height of the pyramid.
In this problem, B+=+sqrt%28S%28S-a%29%28S-b%29%28S-c%29%29 using Heron's formuls for the area of a triangle when the three sides are known. S = Semi-perimeter = 30/2 = 15,
a = b = c = 10, so...
B+=+sqrt%2815%28125%29%29
B+=+sqrt%281875%29
B+=+43.3
So the volume of the pyramid is:
V+=+43.3%286%29%2F3
V+=+86.6Cubic feet.