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Question

ABCDEF is a regular hexagon with centre O. If area of triangle OAB is 9cm2, find the area of the circle in which the hexagon is inscribed.
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Solution

Given: Area of OAB=9cm2

We know that a regular hexagon is made up of 6 equilateral triangles.

But area of each equilateral triangle =9

34×(side)2=9

(side)2=363

For the circle in which the hexagon is inscribed, its radius r= side of the hexagon

Now, Area of a circle =πr2

Area of a circle =227×363

Area of a circle =65.32cm2

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