Question

a right pyramid with a square base has a base edge length of 24 feet and a slant height of 20 feet. what is the height of the pyramid? 4 feet 8 feet 12 feet 16 feet

Explanation:

Step1: Find half of the base - edge length

The base - edge length is 24 feet. Half of it is $\frac{24}{2}=12$ feet.

Step2: Use the Pythagorean theorem

The slant height $l = 20$ feet, and the base of the right - triangle formed (half of the base - edge) is $a = 12$ feet. Let the height of the pyramid be $h$. According to the Pythagorean theorem $h=\sqrt{l^{2}-a^{2}}$.
Substitute $l = 20$ and $a = 12$ into the formula: $h=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}=\sqrt{32\times8}=\sqrt{256}=16$ feet.

Answer:

16 feet