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)
)
Frage
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.
Lösung
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)
)