Q33 of 37 Page 13

Find the difference between the area of a regular hexagonal plot each of whose side is 72 m and the area of the circular swimming tank inscribed in it.


The side of hexagonal plot = 72m




= 1296√3cm2


∴ Area of hexagonal plot = 6 × Area of triangle OAB


= 6 × 1296√3


= 7776(1.732)


=13468.032m2


In ΔOCA, by Pythagoras theorem


(Hypotenuse)2 = (Perpendicular)2 + (Base)2


(OA)2 = (OC)2 + (AC)2


⇒ (72)2 = (OC)2 + (36)2


⇒ (OC)2 = 5184 – 1296


⇒ (OC)2 = 3888


⇒ r2 = 3888


∴Area of inscribed circular swimming tank = πr2



= 12219.429m2


∴ Required difference = 13468.032 – 12219.429


= 1248.603m2


Hence, the difference between the area of a regular hexagonal plot and the area of the circular swimming tank inscribed in it is 1248.60.3m2


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