Question

What is the area of a regular octagon with a side length of 6 mm and an apothem length of 7.243 mm? Round your answer to the nearest hundredth.

Answer 1

OCTA=8, an octagon has 8 sides, thus if one side is 6mm, then all sides, namely the perimeter, is 6+6+6+6+6+6+6+6, or 48.

now, we know what the apothem is.

$\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ -------\\ p=48\\ a=7.243 \end{cases}\implies A=\cfrac{1}{2}(7.243)(48)$