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# Abcdef is a Regular Hexagon with Centre O (In the Following Figure). If the Area of Triangle Oab is 9 Cm2, Find the Area of : (I) the Hexagon and (Ii) the Circle in Which the Haxagon is Incribed. - Mathematics

Sum

ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm2, find the area of : (i) the hexagon and (ii) the circle in which the haxagon is incribed.

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#### Solution

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

We have given area of the one of the triangles.

∴"Area of the hexagon=6xx area of one equilateral triangle"

∴"Area of the hexagon"=6xx9

∴"Area of the hexagon"=54

We know that if a regular hexagon is inscribed in the circle, then the radius of the circle is same as the side of the regular hexagon.

We also know that a regular hexagon is made up of 6 equilateral triangles and we have area of one of the equilateral triangle.

∴"Area of the equilateral triangle"=sqrt3/4 xx"side"^2

Substituting the value of the given equilateral triangle we get,

∴9=sqrt3/4xx"side"^2

∴ side^2=(9xx4)/sqrt3

∴ "side"^2=36/sqrt3

Now we will find the area of the circle.

∴ Area of the circle=pi r^2

Substituting the values we get,

∴" Area of the circle"=22/7xx36/sqrt3

Now we will substitute sqrt3=1.732 we get,

∴" Area of the circle"=22/7xx36/1.732

∴" Area of the circle"=792/12.124

∴" Area of the circle"=65.324

Therefore, area of the hexagon and area of the circle are 54 cm^2 and 65.324 cm^2

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.4 | Q 29 | Page 60
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