Question

Find the area of an inscribed 100-gon if the radius of the circle is 1 unit.

Answer 1

Interesting problem here. Alright, so for a regular polygon, the formula to determine the area is this : A = n * (a * s)/2, where s is the length of a side and a is the apothem. Now we need to find the side and apothem. We have the following :

Answer 2

(the triangle on the right is one portion of the 100-gon) So, we have the hypotenuse of a right triangle and we can determine the angle at the center. Since all triangles are the same, they all have the same angle. The sum of all these angles will be 360 degrees, so each angle will be worth 3.6 degrees. So far so good?

Answer 3

so, knowing all of this, how would you determine the missing values from your area formula, i.e. apothem and side length?

Answer 4

What is the sum of the side? How would I find the perimeter of the 100-gon?

Answer 5

Area of the circle is radius^2*pi
which is just pi... then I

Answer 6

Why is it 360 degrees?

Answer 7

come back baby

Answer 8

i need you

Answer 9

Me or him? I'm confuzzled

Answer 10

you please :"} Why is the sum of all the angles equal to 360 degrees?

Answer 11

shouldnt it be (100-2)180/100?

Answer 12

2pi, 360 degrees, I guess it's just a matter of what units you prefer to work in. if you have an hexagon, you get the following :

where x is the angle at the center for one triangle and y is the full angle for the circle. As we can see, y = 6 x, because there are 6 sides. Now y can be worth 360 degrees, 2pi rad or even 400 grad if that floats your boat, but x will always be y/number of sides. makes sense?