Mathematics Question and Solution
Calculating Shaded Area Blue.
a² = 4²+3²
a = √(25)
a = 5 units.
a is the radius of the quarter circle.
5 ~ 4
3 ~ b
Cross Multiply.
5b = 12
b = 2.4 units.
d² = 5²+3²
d = √(34) units.
tane = 3/4
e = atan(¾)°
f² = 4²+2.4²
f = 4.66476151588 units.
g = d-f
g = 1.16619037897 units
tanh = 4/2.4
h = atan(5/3)°
j = 180-h
j = (180-atan(5/3))°
Area Blue is;
(0.5*2.4*1.16619037897sin(180-atan(5/3)))+(atan(3/4)π*5²÷360)-(0.5*5²sin(atan(3/4))
= 1.2+8.04376385992-7.5
= 1.74376385992 square units.
