Mathematics Question and Solution
Calculating area of the half circle.
Notice.
8π cm² is the area of the red inscribed circle.
πr² = 8π
r = √(8)
r = 2√(2) cm.
r is the radius of the red inscribed circle.
Let x be that radius of the half circle.
a = x+r
a = (x+2√(2)) cm.
b = x-r
b = (x-2√(2)) cm.
Calculating x.
a² = b²+x²
(x+2√(2))² = (x-2√(2))²+x²
x²+4√(2)x+8 = x²-4√(2)x+8+x²
4√(2)x = x²-4√(2)x
8√(2)x = x²
x = 8√(2) cm.
Again, x is the radius of the half circle.
Therefore, area half circle is;
½(πx²)
= ½*π*(8√(2))²
= ½*π*64*2
= 64π cm²
