Mathematics Question and Solution
tana = 1/2
a = atan(1/2)°
b = 180-2a
b = (180-2atan(½))°
Notice!
Radius of the inscribed circle is 1 unit.
Area yellow is;
Area triangle with height 2 units and base 1 unit - Area square with side 1 unit + Area quarter circle with radius 1 unit - Area sector with radius 1 unit and angle (180-2atan(½))° + Area triangle with height 1 unit and base (180-2atan(½)) units.
= (½*2*1)-(1*1)+(0.25π*1*1)-((180-2atan(½))π*1*1/360)+(0.5*1*1sin(180-2atan(½)))
= 1-1+0.7853981634-1.1071487178+0.4
= 1.1853981634-1.1071487178
= 0.0782494456 square units.
= 0.078 square units to 3 decimal places.
