Question

For the square pyramid, the lateral edge length is 25 inches and the slant height is 24 inches find the height of the pyramid H round your answer to the nearest whole number hint before finding the length of age 1st need to find the length of r

Answer 1

To find the height of the pyramid, we can use the Pythagorean theorem.

Let r be the length of one side of the square base.
Let H be the height of the pyramid.

According to the hint, we first need to find the length of r. Since the lateral edge length is 25 inches and the square base has four equal sides, the length of one side of the square base is 25/4 inches.

Now, let's use the Pythagorean theorem to find the length of H. We have a right triangle with the slant height (24 inches), one-half of the base side (r/2 inches), and the height (H inches).

Using Pythagorean theorem, we have:
(H)^2 = (r/2)^2 + (24)^2
H^2 = (r^2/4) + 576
H^2 = (r^2 + 2304)/4

To further solve for H, we need to find the value of r. We already know that r = 25/4.

Now, substitute the value of r into the equation:
H^2 = ((25/4)^2 + 2304)/4

H^2 = (625/16 + 2304)/4
H^2 = (625 + 2304*16)/16*4
H^2 = (625 + 36864)/64
H^2 = 37489/64

H = sqrt(37489)/sqrt(64)
H ≈ 6.08

Rounding H to the nearest whole number, we get:
H ≈ 6 inches.

Therefore, the height of the pyramid is approximately 6 inches.