Question

32. The diagram shows a part of the perimeter of a regular
polygon with n sides
The centre of the polygon is at O and OA = OB = 1 unit
a) What is the angle AOB in terms of n?
b) Work out an expression in terms of n for the area
of the polygon.​

Answer 1

Given : a regular  polygon with n sides   The centre of the polygon is at O and OA = OB = 1 unit

To Find :  a) What is the angle AOB in terms of n?

b) Work out an expression in terms of n for the area  of the polygon.​

Solution:

Central Angle = 360°

∠AOB = 360°/n

n = number of sides

∠AOB = 360°/n  

Area of one triangle = (1/2)*OA * OB  * Sin∠AOB

=> Area of one triangle = (1/2)(1)(1)Sin(360°/n )

=> Area of one triangle = (1/2)Sin(360°/n )

Area of polygon = number of triangles *  Area of one triangle

=> Area of polygon =  (n/2)Sin(360°/n )

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Answer 2

we get two congruent triangles each of angle 180/n