سؤال

Let's have a circle with radius r.

I want to find out the area of the hexagon drawn around the circle. Supplemented is a sample image except I need to whole are of hexagon, not just intersection.

Area of hexagon drawn inside circle is:

(sqrt3*r)^2

as far as I know.

enter image description here

هل كانت مفيدة؟

المحلول

This hexagon consists of 6 equilateral triangles with height R. Area of such triangle is

s = R * R * Sqrt(3) / 3

Area of hexagon

S = 6 * s = 2 * Sqrt(3) * R^2

(If you need area of colored region, it is R^2 * (2 * Sqrt(3) - Pi))

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