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 base edge length

The base is a square with edge 24 ft, so half the edge is $\frac{24}{2}=12$ ft.

Step2: Use Pythagorean theorem

The slant height (20 ft), half base edge (12 ft), and pyramid height $h$ form a right triangle. Apply $h=\sqrt{l^2 - s^2}$, where $l$ is slant height, $s$ is half base edge.
$h=\sqrt{20^2 - 12^2}=\sqrt{400 - 144}=\sqrt{256}$

Step3: Calculate square root

$\sqrt{256}=16$

Answer:

16 feet