# Apothem

• Aug 20th 2008, 04:38 PM
topaz192
Apothem
I understand how to find the apothem, but i dont know what to do with it afterwards.

If the apothem of a regualr pentagon is 10.8 what would be the radius of the circumscribed circle?

my book doesnt say much on solving this...

and how would you find length and perimeter?
• Aug 20th 2008, 05:19 PM
galactus
The apothem is the distance from the center to the midpoint of a side of the pentagon. So, if we draw that line and one to the corner of the pentagon(which is the radius of the circle) we get a right triangle.

The angle of this right triangle is 36 degrees = Pi/5 radians. See why?.

$radius=10.8sec(\frac{\pi}{5})=\frac{10.8}{cos(\fra c{\pi}{5})}$

The length of a side of the pentagon would be $21.6tan(36)$

We could also get it from the radius we found by using sine: $21.6sec(36)sin(36)$
• Aug 20th 2008, 05:24 PM
topaz192
i see where you got 36. [ 360 divided by 10 ]
where did 5 come from?
• Aug 20th 2008, 05:26 PM
galactus
Which 5?. The Pi/5?. That is just the radian equivalent of 36 degrees. Whatever you want to use.

The 5.4 came from making a mistake. I fix. That should be 21.6
• Aug 20th 2008, 05:26 PM
topaz192
i dont understand (Crying)
...how do you find the radius?
• Aug 20th 2008, 05:30 PM
galactus
I just showed you. It's just a little trig. Look at the triangle.
• Aug 20th 2008, 05:31 PM
topaz192
i understand how you found the length and perimeter i dont understand the radius. the formula is confusing
• Aug 20th 2008, 05:34 PM
topaz192
Quote:

Originally Posted by galactus
Which 5?. The Pi/5?. That is just the radian equivalent of 36 degrees. Whatever you want to use.

The 5.4 came from making a mistake. I fix. That should be 21.6

oooohh ok i see now. i just read the mistake.