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Question


A 6 sided regular polygon (hexagon) is inscribed in a circle of radius 10 cm, find area of the hexagon. [2 MARKS]

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Solution

Solution: 2 Marks

AOB=3606=60

Since OA = OB = 10 cm, triangle OAB is isosceles which gives

OAB=OBA

So, all three angles of the triangle are equal and therefore it is an equilateral triangle. Hence

AB = OA = OB = 10 cm.

Area of an equilateral triangle of side a is =34×(a)2

Therefore, Area of the equilateral triangle AOB
=34×(10)2

=43.30 cm2

Area of hexagon
=6×area of one equilateral triangle

=6×43.30

=259.8 cm2


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