Question

The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Check all that apply.

Answer 1

The length of segment XY can be found by solving for a in

`20^2-7.65^2=a^2`

The measure of the central angle
`\angle ZXW` is
`45\degree`.

Explanation:

If the regular octagon has a perimeter of 122.4cm, then each side is
`(122.4)/(8)=15.3cm`

The measure of each central angle is
`(360\degree)/(8)=45\degree`

The angle between the apothem and the radius is
`(45)/(2)=22.5\degree`

The segment XY=a is the height of the right isosceles triangle.

We can use the Pythagoras Theorem with right triangle XYZ to get:

`a^2+7.65^2=20^2`

`a^2=20^2-7.65^2`

Therefore, the correct options are:

The length of segment XY can be found by solving for a in

`20^2-7.65^2=a^2`

The measure of the central angle
`\angle ZXW` is
`45\degree`.