Mathematics Question and Solution
Calculating yellow area.
Notice.
Area of the ascribed square is 12 square units.
Area yellow is;
½(12) - (½(⅔√(3))²sin(atan(3))÷sin(135-atan(3)))sin(45)
= 6 - (½)
= ½(12-1)
= ½(11) square units.
= 5.5 square units.
Or
Calculating Yellow Area.
Let a be the side length of the square.
a² = 12
a = √(12) = 2√(3) units.
a = 3x
x = ⅓(2√(3)) units.
x = 1.15470053838 units.
tanb = 3x/x
b = atan(3)°
b = 71.5650511771°
c = 180-45-b
c = 180-45-71.5650511771
c = 63.4349488229°
(d/sin71.5650511771) = (1.15470053838/sin63.4349488229)
d = 1.22474487139 units.
e = 0.5*1.22474487139*1.15470053838sin45
e = 0.5 square units.
e is the red area.
Therefore, area yellow is;
½(12)-e
= 6-0.5
= 5.5 square units.
