Mathematics Question and Solution
a = ½(12)
a = 6 cm.
a is the radius of the inscribed half circle.
c = (6+b) cm.
b is the radius of the inscribed circle.
d = (12-b) cm.
Calculating b.
(6+b)²+6² = (12-b)²
36+12b+b²+36 = 144-24b+b²
72+12b = 144-24b
36b = 72
b = 2 cm.
Again, b is the radius of the inscribed circle.
e²+6² = 12²
e² = 144-36
e = √(108)
e = 6√(3) cm.
Painted Area is;
2(area sector with radius 12 cm and angle 60°) - Area triangle with height 6√(3) cm and base 12 cm + Area half circle with radius 6 cm - Area circle with radius 2 cm.
= 2(60π*12*12/360)-(0.5*12*6√(3))-(0.5*π*6*6)-(π*2*2)
= 48π-36√(3)-18π-4π
= 26π-36√(3)
= 2(13-18√(3)) cm²
= 19.3275799209 cm²
