Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side let of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
It implies;
Area R is;
Area trapezoid with parallel sides 1 unit and 1.44948974279 unit, and height 2 unit - Area square with side 1 unit - Area triangle with base and height 1 unit respectively - Area sector with radius √(2) unit and angle 32.3335306935° - Area triangle with height √(2) unit and base 0.3178372452 unit
= (½*2(1+1.44948974279)) - (1*1) - (½*1*1) - (32.3335306935*π*√(2)²÷360) - (½*√(2)*0.3178372452)
= 2.44948974279 - 1 - 0.5 - 0.5643265694 - 0.22474487139
= 0.160418302
Therefore;
Area Square ÷ Area R to 1 decimal place is;
4 ÷ 0.160418302
= 24.9348107425
≈ 24.9
