Mathematics Question and Solution
Notice!
The side length of the inscribed biggest square is 5 units.
Calculating inscribed red area.
tana = 2.5/5
a = atan(½)°
b = 2atan(½)°
tanc = 5/2.5
c = atan(2)°
d = 2atan(2)°
Therefore, area red is;
Area sector with radius 2.5 units and angle 2atan(2) - Area triangle with height 2.5 units and base 2.5sin(2atan(2)) units + Area sector with radius 5 units and angle 2atan(½) - Area triangle with height 5 units and base 5sin(2atan(½)) units - 2(area quarter circle with radius 2.5 units + area triangle with height and base 2.5 units each).
= (2atan(2)π*2.5*2.5÷360)-(0.5*2.5*2.5sin(2atan(2))+(2atan(½)π*5*5÷360)-(0.5*5*5sin(2atan(½))-2((¼*2.5*2.5π)-(0.5*2.5*2.5))
= 6.9196794862-2.5+11.591190225-10-2(4.9087385212-3.125)
= 6.9196794862-2.5+11.591190225-10-9.8174770424+6.25
= 2.4433926688 square units.
