Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the radius of the semi circle be 3 units.
Therefore shaded area ÷ area square will be;
(½(area quarter circle of radius 3 units - area triangle of height and width 3 units respectively) + area triangle of two sides ((3√(2)/2)-(3√(3)tan22.5)/2) units and ((3√(2)/2)-(3√(3)tan22.5)/2)xsin(tan–¹(3)-45)÷sin(180-tan–¹(3))) units, and the angle they form, angle 45°) ÷ (area square of single side length ½(3√(2)) units).
{½((9π/4)-(9/2)) + ((3√(2)/2)-(3√(3)tan22.5)/2)²xsin(tan–¹(3)-45)÷sin(180-tan–¹(3))x0.5sin45}÷{½(3√(2))}²
= ((9π/8)-(9/4)+(0.25735931288))÷(½(3√(2)))²
= (1.54165104817)÷(½(3√(2)))²
= 0.34258912182
≈ 0.343
