Question

The measure of a central angle of a regular polygon is 18 degrees, how many sides does it have?
a. 20
b. 18.
c. 16

Answer 1

The general rule is

Central angle = 360/n

where n is the number of sides

Answer 2

so it's 20?

Answer 3

You got it. Nice work.

Answer 4

Thank you!

Answer 5

you're welcome

Answer 6

Can you help with the next one?

Answer 7

sure

Answer 8

What is the measure of each angle in a 12 sided polygon.
a. 90
b. 30
c. 150

Answer 9

In this case, you can use the formula


A = 180(n-2)/n


where A is the measure of each angle and n is the number of sides. So in this case, n = 12.

Answer 10

So 150?

Answer 11

you nailed it

Answer 12

Yay! thanks!

Answer 13

yw

Answer 14

What is an apothem?

Answer 15

it's the line segment from the center of a polygon to the midpoint of one of the sides

Answer 16

Find the apothem of a regular polygon with an area of 625m^2 and perimeter of 100 m

Answer 17

the green line shown in the pic (see the link) is the apothem

http://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Apothem_of_hexagon.svg/220px-Apothem_of_hexagon.svg.png

Answer 18

a. 12
b. 10
c. 12.5

Answer 19

how many sides does this polygon have? does it say?

Answer 20

oh wait, nvm I think we can figure that out, one sec

Answer 21

No. just says it's a regular polygon.

Answer 22

Well if there are n sides and the perimeter is 100, then each side is 100/n

Answer 23

Take half that to get (1/2)*(100/n) = 100/(2n)

So half of one side is 100/(2n)

Answer 24

Now if we break up the polygon, we get a bunch of triangles. We get n of them in fact. Here's one such triangle