Mathematics Question and Solution
Let the radius of the circle be r.
Calculating r.
2(½*12r)+(r*r)+2(½*8r) = ½(12+r)(8+r)
(12r)+r²+(8r) = ½(12+r)(8+r)
24r+2r²+16r = 96+20r+r²
40r+2r² = 96+20r+r²
r²+20r-96 = 0
(r+10)² = 96+100
r = -10±√(196)
r = -10±14
It implies;
r ≠ -24
r = 4 cm.
Therefore, the height (h) and base (b) of the ascribed right-angled triangle is;
h = 12+4 = 16 cm.
b = 8+4 = 12 cm.
Green painted area is;
Area triangle with height 16 cm and base 12 cm - Area circle with radius 4 cm.
= ½(16*12)-π(4)²
= 96-16π
= 16(6-π) cm²
= 45.7345175426 cm²
