Question

For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number The height of the square pyramid is?

Answer 1

We can use the Pythagorean theorem to solve for the height of the square pyramid.

The lateral edge length, e, represents the length of the base of the square pyramid. Since it is a square, all sides are equal and each side length is also 25 in.

Let's call the height of the pyramid h. One face of the pyramid is a right triangle with legs of length h and e/2 (half the length of the base). The slant height, s, is the hypotenuse of this right triangle.

So we can use the Pythagorean theorem: h^2 + (e/2)^2 = s^2

Plugging in the given values, we get: h^2 + (25/2)^2 = 24^2

Simplifying: h^2 + 625/4 = 576

Multiplying both sides by 4 to get rid of the fraction: 4h^2 + 625 = 2304

Subtracting 625 from both sides: 4h^2 = 1679

Dividing both sides by 4: h^2 = 1679/4

Taking the square root of both sides: h = sqrt(1679/4)

Rounding to the nearest whole number: h ≈ 32

So the height of the square pyramid is approximately 32 inches.