Question

Find the area of a regular octagon with an apothem of 7 inches and a side length of 5.8 inches. (nearest tenth)

[ ? ] in^2

Answer 1

162.4 in²

Explanation:

LETS GET INTOOOOEEETTT

Let's start with what we know:

Area of regular octagon = 1/2 x perimeter x apothem

We know the apothem, so all that we need to find to fill in the above equation is the perimeter:

perimeter = 8 x 5.8 = 46.4in

Now we can fill in our original equation and solve:

Area of regular octagon = 1/2 x perimeter x apothem

Formula = n (s/2)² divided by tan( π /n)

= 8 (5.8/2)² divided by tan ( π /8)

= 162.4283 in²

ORRR when rounded to the nearest tenth,

=162.4 in²