Mathematics Question and Solution
Let r be the radius of the semi circle.
Calculating r.
√(r²-49)+√(r²-36) = 12
r²-49 = (12-√(r²-36))²
r²-49 = 144-24√(r²-36)+r²-36
24√(r²-36) = 144+13
24√(r²-36) = 157
r²-36 = (157/24)²
r² = (157/24)²+36
r² = 45385/576
r = √(45385/576)
r = √(45385)/24 units.
r = 8.87656480728 units
Green Area is;
Area semi circle with radius 8.87656480728 units - Area inscribed rectangle with length and width 12 units and 6 units respectively.
= 0.5(45385/576)π-(12*6)
= (45385/1152)π-72
= (45385π-82944)/1152 square units.
= 51.7683876591 square units.
