a right pyramid with a square base has a base edge length of 24 feet and a slant height of 20 feet. what is…

Explanation:

Step1: Find half - base length

The base is a square with edge length 24 ft. Half of the base edge length $a=\frac{24}{2}=12$ ft.

Step2: Use Pythagorean theorem

Let the height of the pyramid be $h$, the slant height $l = 20$ ft and half - base length $a = 12$ ft. According to the Pythagorean theorem in the right - triangle formed by the height, half of the base edge and the slant height ($l^{2}=h^{2}+a^{2}$), we can solve for $h$. So $h=\sqrt{l^{2}-a^{2}}$. Substitute $l = 20$ and $a = 12$ into the formula: $h=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}=\sqrt{32\times8}=\sqrt{256}=16$ ft.

Answer:

16 feet