Question

A regular octagonal pyramid has base edge 3 m and lateral area 60 m². Find its slant height.

Short answer

The slant height of the pyramid is5 m.

Step-by-step solution

Step 1. Given information.

Base edge of pyramid is 3 m and lateral area is 60 m².

Step 2. Write the concept.

The volume of the pyramid is given by the following formula:

$\text{L.A.}=\frac{1}{2}pl$

Step 3. Determine the height.

Substitute the given values in the formula.

$\begin{array}{c}\text{L.A.}=\frac{1}{2}pl\\ 60=\frac{1}{2}\left(8\left(3\right)\right)\left(l\right)\text{[substituteand}p=nb]\\ 60=12l\text{[multiplyanddivide]}\\ l=5\text{[divide]}\end{array}$