Mathematics Question and Solution
Calculating Area Yellow.
½*a²sin60 = 24
√(3)a² = 24*4
a² = 96/√(3)
a = √(96/√(3))
a = 7.44483887282 units.
a is the radius of the circle.
b = a-x
b = (7.44483887282-x) units.
Calculating x.
tan60 = (7.44483887282-x)/x
√(3)x = (7.44483887282-x)
(√(3)+1)x = 7.44483887282
x = 7.44483887282/(√(3)+1)
x = 2.72500015453 units.
cos30 = x/c
c = 2.72500015453/cos30
c = 3.14655914552 units.
d = a-c
d = 7.44483887282-3.14655914552
d = 4.2982797273 units.
It implies, area yellow is;
0.5d²sin60
= 0.5*4.2982797273²sin60
= 8 square units.
