Mathematics Question and Solution
Radius of the half circle is 5 units.
5² = 4²+a²
a = 3 cm.
tanb = 4/3
b = atan(4/3)°
c = 2b
c = 2atan(4/3)°
5² = 3²+d²
d = √(25-9)
d = 4 cm.
tane = 3/4
e = atan(3/4)°
f = 2e
f = 2atan(3/4)°
Shaded Area is;
Area sector with radius 5 cm and angle 2atan(4/3)° - Area triangle with height 5 cm and base 5sin(2atan(4/3)) cm - Area sector with radius 5 cm and angle 2atan(3/4)° + Area triangle with height 5 cm and base 5sin(2atan(3/4)) cm.
= (2atan(4/3)π*5*5/360)-(0.5*5*5sin(2atan(4/3))-(2atan(3/4)π*5*5/360)+(0.5*5*5sin(2atan(3/4))
= 23.18238045-12-16.0875277198+12
= 23.18238045-16.0875277198
= 7.0948527302 cm²
