Mathematics Question and Solution
Let the single side length of the equilateral triangle be 4 unit.
Therefore;
Shaded area ÷ Area circle exactly in decimal is;
(Area sector with radius √(3) unit and angle (180-2(sin–¹(sin60÷√(13))+30)) - Area isosceles triangle with two equal length √(3) unit and the angle they form, angle (180-2(sin–¹(sin60/√(13))+30))) ÷ (Area circle of radius √(3) unit).
= ((180-2(sin–¹(sin60÷√(13))+30))xπ(√(3))²÷360 - ½((√(3))²xsin(180-2(sin–¹(sin60÷√(13))+30)))) ÷ (3π)
= (2.4139010313 - 1.49889012193) ÷ 3π
= (0.91501090937) ÷ 3π
= 0.0970856728
