Question

If a regular octagon has side lengths 10.9 inches and perimeter of octagon is 87.2 inches and area is 392.4 inches. second octagon has side lengths equal to 5.45 inches. find area of second octagon.

Answer 1

The area of a regular \(n\)-gon is
\[A=\frac{ap}{2}\]
where \(p\) is the perimeter and \(a\) is the length of the apothem. You can solve for the apothem of the first octagon.

Then you would establish a ratio between the apothem/perimeters of each octagon:
\[\frac{a_1}{p_1}=\frac{a_2}{p_2}\]
We know some of this information already:
\[\frac{\frac{2(392.4)}{87.2}}{87.2}=\frac{a_2}{8(5.45)}\]
Solve for \(a_2\), then find the area,
\[A_2=\frac{a_2p_2}{2}\]

Answer 2

is the area of second octagon 98.1 inches

Answer 3

Just a sec, let me compute that.

Answer 4

Yes that's right.

Answer 5

thanks

Answer 6

You're welcome