A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio

Question

2 years ago

14

of the area of the larger hexagon to the area of the smaller hexagon

1 answer:

Anna007 [38] · Answer 1 · 2023-04-12T23:33:58+03:00

4/3 of the area of the larger hexagon to the area of the smaller hexagon

Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.

The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)

The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3

area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18

= 4/3

Required ratio = 4/3 answer

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