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. hint: before finding the length of $h$, you will first need to find the length of $r$. (1 point)

Explanation:

Step1: Find $r$ via Pythagoras

$$\begin{align} r &= \sqrt{e^2 - s^2} \\ &= \sqrt{25^2 - 24^2} \\ &= \sqrt{625 - 576} \\ &= \sqrt{49} \\ &= 7 \end{align}$$

Step2: Find $h$ via Pythagoras

$$\begin{align} h &= \sqrt{s^2 - r^2} \\ &= \sqrt{24^2 - 7^2} \\ &= \sqrt{576 - 49} \\ &= \sqrt{527} \\ &\approx 23 \end{align}$$

Answer:

23 inches