Question 1113996: A square pyramid has slant edges of 15cm and a perpendicular height of 12 cm.
Find the surface area of the pyramid.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
We have to assume the pyramid is a right square pyramid; if the peak is not directly above the center of the base, then we can't determine the surface area.
Consider the right triangle formed by the peak of the pyramid, the center of the base, and one corner of the base. That triangle has hypotenuse 15 and one leg 12, so the other leg (distance from the center of the base to one corner of the base) is 9. So the diagonal is the square base if 18; the side length of the base is 9*sqrt(2).
So finding the area of the base is easy.
Each face is an isosceles triangle with side lengths 15, 15, and 9*sqrt(2). You can find the area of each face by drawing the altitude to the base and using the Pythagorean Theorem to find the length of that altitude.
The numbers get ugly, so I'll leave the arithmetic to you....
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