Mathematics Question and Solution
Calculating red area.
tana = 10/5
a = atan(2)°
b = 2a
b = 2atan(2)°
c = 180-b
c = 180-2atan(2)
c = 2atan(½)°
Area red is;
Area sector with radius 5 units and angle 2atan(2)°-Area triangle with height 5 units and base 5sin(2atan(2)) units+Area sector with radius 10 units and angle 2atan(½)°-Area triangle with height 10 units and base 10sin(2atan(½)) units.-2(area quarter circle with radius 5 units -area triangle with height and base 5 units each).
= (2atan(2)π*5²/360)-(0.5*5²sin(2atan(2)))+(2atan(½)π*10²/360)-(0.5*10²sin(2atan(½)))-2((¼*π*5²)-(½*5²))
= 27.6787179449-10+46.3647609001-40-2(19.6349540849-12.5)
= 27.6787179449-10+46.3647609001-40-14.2699081699
= 9.7735706751 square units.
