Mathematics Question and Solution
Calculating Area Green Inscribed Half Circle.
Notice.
Length AM = Length CM.
AN = 2 cm.
Let x be the radius of the inscribed half circle.
a = 2+x+x
a = (2+2x) cm.
a is the radius of the the ascribed sector.
b = ½(a)
b = (1+x) cm.
b is AM = CM.
c = (2+x) cm.
Calculating x.
x²+(1+x)² = (2+x)²
x²+1+2x+x² = 4+4x+x²
x²+1+2x = 4+4x
x²-2x-3 = 0
x²-3x+x-3 = 0
x(x-3)+1(x-3) = 0
(x-3)(x+1) = 0
It implies;
x ≠ -1
x = 3 cm.
Therefore, area inscribed half circle is;
½(πx²)
= ½*π*3*3
= ½(9π) cm²
= 4.5π cm²
