A regular hexagon is inscribed in a circle. What is the ratio of the area of the circle to that of its portion not covered by the hexagons?

a regular hexagon makes an angle of 60 degree at the centre that means the which means its sides will be equals to the radius of the circle. Now you have to do is simply subtract the area of hexagon from the area of the circle. (pie r^2) - (6*area of equilateral triangle) Note: Area of hexagon is equals to the six times the area of equilateral triangle. For e.g- If it is given that the side of the regular hexagon is " A" unit then its area will be 6 times the area of an equilateral triangle with side "A"

(pi*r^2)-(6*√3/4*r^2)

(pi*r^2)-(6*√3/4*r^2)