SOLUTION: 100-gon with a radius of 5 what is the area

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Question 748546: 100-gon with a radius of 5
what is the area
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If you know the radius (distance from the center to a vertex), then area will be:
A=%28r%5E2n%2Asin%28360%2Fn%29%29%2F2 where n is the number of sides and r is the radius
if
r=5
n=100
then
A=%285%5E2%2A100%2Asin%28360%2F100%29%29%2F2
A=%2825%2A100%2Asin%283.6%29%29%2F2
A=%282500%2A0.0627905%29%2F2
A=156.97625%2F2
A=78.5

or, you can do it this way:

A+=+r%5E2%2A+n+%2A+tan%28pi%2Fn%29, where r is the radius and n the number of sides
A=5%5E2%2A100+%2A+tan%28pi%2F100%29
A=2500+%2A+0.0314
A=78.5


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
100-gon with a radius of 5
what is the area
=====================
As the number of sides increases, the area approaches that of a circle.
100 is a lot of sides.
Area+=+pi%2Ar%5E2+=+25%2Api
Area =~ 78.54 sq units