The expression of area of a polygon as .
The area of a polygon is proved.
The area of the polygon is (n-equal sides).
Polygon has n congruent triangles with central angle .
Procedure to draw one of the n congruent triangles in a circle is explained below:
Sketch one of the n congruent triangles in a circle with central angle as shown in Figure 1.
Refer Figure 1.
The angle AOB is divided into 2 right angle triangles with legs of length
Therefore, the triangle has area of (1)
Rearrange Equation (1) as shown below.
The area of the polygon with n equal sides is expressed as follows:
Substitute for in Equation (2).
Therefore, the area of a polygon with n equal sides is equal to .
Therefore, The expression of area of a polygon as .
The value of
The value of is proved.
Refer part (a).
The area of a polygon with n equal sides is .
Find the value of as shown below:
Substitute for in .
As , , Substitute for in Equation (3).
Therefore, the value of is equal to .
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