SOLUTION: A right square pyramid of height h metres has base of side length 10m. If the area of one triangular face of the pyramid is equal to the area of the base, find the value of h

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Question 1125740: A right square pyramid of height h metres has base of side length 10m. If the area of one triangular face of the pyramid is equal to the area of the base, find the value of h
Answer by greenestamps(13203) About Me  (Show Source):
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The area of the square base is 100.

The base of each triangular face is 10; if the area of each triangular face is equal to the area of the base of the pyramid (100), then the altitude, a, of each triangular face can be calculated from the formula for the area of a triangle:

100+=+%281%2F2%29%2810%29%28a%29

So the altitude of each triangular face is 20.

Each of those altitudes, along with the height of the pyramid and half the width of the square base, forms a right triangle, with the altitude of the triangle as the hypotenuse. Then the height of the pyramid is given by the Pythagorean Theorem:

h+=+sqrt%2820%5E2-5%5E2%29+=+sqrt%28375%29+=+5%2Asqrt%2815%29

The height of the pyramid is 5*sqrt(15) meters.