Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side length of the square be 1 unit.
Therefore;
Area square is;
1² = 1 square units.
It implies;
Area R is;
Area square - Area equilateral triangle with side 1 unit - 2(area sector with radius 1 unit and angle 30°)
= 1 - ½(sin60) - 2(30π÷360)
= 1 - ¼(√(3)) - (π/6)
= (12-3√(3)-2π)/12 square units.
Therefore;
Area R ÷ Area Square as a single fraction in terms of π is;
(12-3√(3)-2π)/12 ÷ 1
= (12-3√(3)-2π)/12
