Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
Radius of the inscribed circle, r is;
sin52.5 = r/1.04420953776
r = 0.82842712475 unit.
Shaded Area is;
2(area triangle with height 0.63567449039 units and base 0.82842712475 units) - Area sector with radius 0.82842712475 and angle 75°.
= 2(½*0.63567449039*0.82842712475) - (75π*0.82842712475²÷360)
= 0.52660999035 - 0.44917673705
= 0.0774332533 square units.
It implies;
Shaded Area ÷ Area Square to 3 decimal places is;
0.0774332533 ÷ 4
= 0.01935831332
≈ 0.019
