1. 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?

2. 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: $21.6sec(36)sin(36)$

3. i see where you got 36. [ 360 divided by 10 ]
where did 5 come from?

4. 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

5. i dont understand
...how do you find the radius?

6. I just showed you. It's just a little trig. Look at the triangle.

7. i understand how you found the length and perimeter i dont understand the radius. the formula is confusing

8. 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.