Question

What is the apothem and perimeter of a decagon inside a circle if the area is 25 times pi ?

Answer 1

owait, nvm :s

Find the radius of the circle first :D

Answer 2

http://puu.sh/q9Ii
There, once you found the radius, you get this, find the angle between the two r's, (hint: decagon, circle, 360*) then use the cos' law to find the base's measure, and then... and then.. you've got everything to solve this, good luck! ;D

Answer 3

Thanks! didnt give me a radius though!

Answer 4

Aha! You must find the radius by yourself! ^_^ What's the formula to find a circle's radius?

Answer 5

No clue... :/

Answer 6

A circle's radius is pi * r^2

Answer 7

We know that the area is 25pi

So set pi * r^2 equal to 25pi

25 pi = pi r*2
Solve it, and you'll find the radius :)

Answer 8

25 pi = pi r*2
25 = r^2
r = sqrt(25)
r= 5

For the angle, since it's a decagon, you divide 360 by 10, making 36 degrees.

Now you have an angle and two measures by its side
c^2 = a^2 + b^2 - 2ab cos(C)
By using the law of cosine, the base measures ~7.5

Answer 9

Thanks so much!

Answer 10

Now you have the base, find the apothem using the pythagorean theorem, good luck ;D

Answer 11

Thanks. :)