Question

area of a regular polygon with 100 sides and a perimeter of 100 units

Answer 1

The area is 795.5 sq units.

We first find the apothem, using the formula:
$a=\frac{s}{2\tan{(\frac{180}{n})}}$

Since there are 100 sides, all sides are equal and the perimeter is 100, the side length, s, is 1:
$a=\frac{1}{2\tan{(\frac{180}{100})}}=15.91$

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.

Answer 2

The Area of Regular Polygon = 795.5sq.units

What is Polygon?

Polygon is a closed figure where the sides are all side segments. Each sides must intersect with two other sides but only at their End points.

According to the question,

Area of Regular Polygon = (number of sides × length of one sides × apothem)/2

First we find length of apothem (a) = s/2tan($\frac{180}{n}$)

length of one side (s) = 1

Number of sides (n) = 100

Area of Regular Polygon =  (1 × 100 × 15.91)/2 = 795.5sq.units

Hence, Area of Regular Polygon = 795.5sq.units

To learn more about Regular Polygon here

https://brainly.com/question/22412096

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