A regular hexagon (H1) of side 8 cm is inscribed in a circle(C1). Another circle(C2) is inscribed in the regular hexagon (H1) and it circumscribes another regular hexagon(H2) and so on. Find the sum of the areas of all such possible regular hexagons.a)384andradic;3b)288andradic;3c)192andradic;3d)96andradic;3Correct answer is option 'A'. Can you explain this answer?

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A regular hexagon (H₁) of side 8 cm is inscribed in a circle(C₁). Another circle(C₂) is inscribed in the regular hexagon (H₁) and it circumscribes another regular hexagon(H₂) and so on. Find the sum of the areas of all such possible regular hexagons.

a)
384√3
b)
288√3
c)
192√3
d)
96√3

Correct answer is option 'A'. Can you explain this answer?

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A regular hexagon (H1) of side 8 cm is inscribed in a circle(C1). Anot...

Radius of C₁ = 8
Side of the regular hexagon(H₂) = radius of the circle(C₂) = the perpendicular distance from the centre to the base of the hexagon, which is the height of the equilateral triangle whose side is 8.

Hence, the side of the n^th hexagon is √3/2 times the side of the (n-1)^th hexagon.
Hence the required sum

This is in GP with the first term as

and common ratio 3/4.
Sum to infinite terms of the GP

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A regular hexagon (H1) of side 8 cm is inscribed in a circle(C1). Another circle(C2) is inscribed in the regular hexagon (H1) and it circumscribes another regular hexagon(H2) and so on. Find the sum of the areas of all such possible regular hexagons.a)384√3b)288√3c)192√3d)96√3Correct answer is option 'A'. Can you explain this answer?

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