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Rainbow [258]
2 years ago
14

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

of the area of the larger hexagon to the area of the smaller hexagon
Mathematics
1 answer:
Anna007 [38]2 years ago
3 0

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

Learn more about Equations:

brainly.com/question/16450098

#SPJ4

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