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The area is 795.5 sq units.
We first find the apothem, using the formula:
Since there are 100 sides, all sides are equal and the perimeter is 100, the side length, s, is 1:
Now we find the area of the polygon. Since there are 100 sides, there will be 100 equal triangles using the center as a vertex. The formula for the area of a triangle is A=1/2bh; in this case, b is s, the side length, and h is a, the apothem. This gives us:
A=100(1/2)(s)(a) = 100(1/2)(1)(15.91) = 795.5.
We first find the apothem, using the formula:
Since there are 100 sides, all sides are equal and the perimeter is 100, the side length, s, is 1:
Now we find the area of the polygon. Since there are 100 sides, there will be 100 equal triangles using the center as a vertex. The formula for the area of a triangle is A=1/2bh; in this case, b is s, the side length, and h is a, the apothem. This gives us:
A=100(1/2)(s)(a) = 100(1/2)(1)(15.91) = 795.5.