Mathematics Question and Solution
Calculating Area Green.
a = 4+6
a = 10 units.
a is the diameter of the ascribed half circle.
b = ½(a)
b = 5 units.
b is the radius of the ascribed half circle.
c = 5-4
c = 1 unit.
Let x be the radius of the inscribed half circle.
d² = 2x²
d = √(2x²)
d = √(2)x units.
e = 180-45
e = 135°
Calculating x
5² = 1²+(√(2)x)²-2*1*√(2)xcos135
25 = 1+2x²+2x
2x²+2x-24 = 0
x²+x-12 = 0
(x+4)(x-3) = 0
It implies;
x ≠ -4 units.
x = 3 units.
Again, x is the radius of the inscribed circle.
Therefore, Area Green is;
Area half circle with radius 5 units - Area half circle with radius 3 units.
½(5²π)-½(3²π)
= ½(25π-9π)
= ½(16π)
= 8π square units.
