SOLUTION: The steeple of a building is in the shape of a regular pyramid with a triangular base.Each of the 3 base sides is 4.6 meters long,and the steeple is 7.0 meters high. Compute the nu

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Question 159331: The steeple of a building is in the shape of a regular pyramid with a triangular base.Each of the 3 base sides is 4.6 meters long,and the steeple is 7.0 meters high. Compute the number of cubic meters of air space contained in the steeple. Round the answer to the nearest cubic meter.
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
volume of a pyramid is %28B%2Ah%29%2F3 where B is the area of the base and h is the altitude.
the base is an equilateral triangle.
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area of an equilateral triangle is %28s%5E2%2Asqrt%283%29%29%2F4 where s is one of the equal sides of the triangle.
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triangle:
s = 4.6 meters (given)
area = %28%284.6%29%5E2%2Asqrt%283%29%29%2F4 = 9.162548772
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pyramid:
B = 9.162548772
h = 7 meters (given)
volume = %289.162548772%2A7%29%2F3 = 21.37928047
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cubic meters of air space contained in the steeple is 21.