A 6 sided regular polygon (hexagon) is inscribed in a circle of radius 10 cm, find area of the hexagon. [2 MARKS]
Solution: 2 Marks
∠AOB=360∘6=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