There are two concentric hexagons. Each of the side of both the hexagons are parallel. -Maths 9th

There are two concentric hexagons. Each of the side of both the hexagons are parallel. -Maths 9th
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1 Answer

Answer :

In the second figure, ΔOPQ is an equilateral triangle as a regular hexagon is divided into six equilateral triangles. ∴ ∠OPC = 60º⇒ \(rac{OC}{OP}\) = sin 60° ⇒ OC = OP sin 60° ⇒ OC = 8 x \(rac{\sqrt3}{2}\) cm = 4√3 cm.Now in similar Δs OPC and OAD, \(rac{OC}{OD}\) = \(rac{OP}{OA}\) ⇒ \(rac{4\sqrt3}{6\sqrt3}\) = \(rac{8}{OA}\)⇒ OA = 12 cm ⇒ AB = OA = 12 cm(∵ OD = OC + 2√3 = 4√3  + 2√3 = 6√3 cm)∴ Required area = Area of outer hexagon – Area of inner hexagon= \(rac{3\sqrt3}{2}\)(122 - 82) cm2 = 120√3 cm2.
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