Mathematics Question and Solution
a² = 6²+3²
a = √(45)
a = 3√(5) units.
a is the square side.
tanb = (6/3)
b = atan(2)°
It implies;
c = atan(½)°
d² = (3√(5))²+(0.5(3√(5)))²
d = (15/2) units.
d is the radius of the arc.
e = (atan(½)+atan(½))°
e is the angle of the sector formed by the arc.
tan(atan(½)) = f/(0.5*3√(5))
f = ¼(3√(5)) units.
g = 3√(5)-¼(3√(5))
g = ¼(9√(5)) units.
sin(atan(½)) = h/(¼(9√(5)))
h = (9/4) units.
cos(atan(½)) = j/(¼(9√(5)))
j = (9/2) units.
Therefore;
Area Shaded exactly as a single fraction is;
((atan(½)+atan(½))π*(15/2)²/360) - ½*½*3√(5)*3√(5) - ½*(9/4)*(9/2)
= ((5πatan(0.5))/16)-¼(45)-(81/16)
= (5πatan(0.5)-180-81)/16
= (5πatan(0.5)-261)/16 square units.
= 9.7676780063 square units exactly in decimal.
