Question

Find the area of a regular octagon with an apothem of 14.5 ft. Round to nearest tenth.

I got 2030.3 ft^2

Answer 1

You know the apothem, being 14.5. You want to find the area.

\(\bf{A=\frac{1}{2}ap}\)

We need to find the perimeter. This means you need to identify the side length. So you would identify the interior angle of an octagon. An octagon has 8 sides. You would divide 360 by 8 to find the interior angle of each side.

\(\bf{360 \div 8 = 45}\)

Now you divide by 2 (so you can solve this with a right triangle).

\(\bf{45 \div 2 = 22.5^{o}}\)

So you have this...



Now solve by right triangle...



You would solve with the tan ratio.

\(\large\bf{tan(22.5)=\frac{a}{14.5}}\)

What would that equal?

Answer 2

6.006
?