Mathematics Question and Solution
Calculating Red Area.
tana = 5/10
a = atan(½)°
b = 2a
b = 2atan(½)°
tanc = 10/5
c = atan(2)°
d = 2c
d = 2atan(2)°
It implies;
Area Red is;
Area sector with radius 5 units and angle 2atan(2)° - (2(area triangle with height 10 units and base 5 units)-area sector with radius 10 units and angle 2atan(½)°) - 2(Area quarter circle with radius 5 units-area triangle with height and base 5 units respectively)
= (2atan(2)π*5*5/360) - (2(0.5*10*5)-(2atan(½)π*10*10/360)) - 2((¼*π*5*5)-½*5*5)
= 27.6787179449-(50-46.3647609001)-2(19.6349540849-12.5)
= 27.6787179449-3.6352390999-14.2699081699
= 9.7735706751 square units.
= 9.774 square units to 3 decimal places.
