Mathematics Question and Solution
Let the three congruent semi circles radius be 2 units.
Calculating radius, r of the ascribed quarter circle.
Let it be a.
2b² = 2²
b = √(2) units.
4²-√(2)² = c
c = √(14) units.
It implies;
a = 2+√(14)+√(2)
a (radius of the ascribed quarter circle) = 7.15587094915 units.
Area Quarter Circle is;
¼(7.15587094915)²π
= 40.21748244675 square units.
Area R is;
40.21748244675 - 2(½*√(14)*√(2)+½*2+(180-atan(√(2/14))*4π/360+(135-atan(√(7))*4π/360)
= 40.21748244675 - 2(2.64575131106+1+5.56045105937+2.29353057461)
= 40.21748244675 - 2(11.49973294504)
= 40.21748244675 - 22.99946589008
= 17.21801655667 square units.
Therefore;
Area R ÷ Area Quarter Circle to 3 decimal places is;
17.21801655667 ÷ 40.21748244675
= 0.42812268469
≈ 0.428
