Mathematics Question and Solution
Calculating area red.
tana = 3/5
a = atan(3/5)°
b = 2a
b = 2atan(3/5)°
tanc = 5/3
c = atan(5/3)°
d = 2c
d = 2atan(5/3)°
Therefore, red area is;
2(area circle with radius 5 units) - 4(area quarter circle with radius 5 units and angle 2atan(3/5)° - area triangle with height 5 units and base 5sin(2atan(3/5)) units) - 4(area quarter circle with radius 3 units and angle 2atan(5/3)° - area triangle with height 3 units and base 3sin(2atan(5/3)) units)
= 2(5²π)-4(2atan(3/5)π*5²/360 - (0.5*5*5sin(2atan(3/5))-4(2atan(5/3)π*3²/360 - (0.5*3*3sin(2atan(5/3))
= 157.0796326795-4(13.5104875068-11.0294117647)-4(9.2733914387-3.9705882353)
= 157.0796326795-54.0419500272+44.1176470588-37.0935657548+15.8823529412
= 125.9441168975 square units.
