Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the ascribed quarter circle radius be 4 units.
Therefore;
Area blue is;
Area triangle with two side 1 unit and 3 units, and angle 2asin(1/3)°
= ½*3sin(2asin(1/3))
= 0.94280904158 space units.
Area red is;
Area triangle with two side 1 unit and 3 units, and angle (180-2asin(1/3))° + Area triangle with two side 2 units and √(44/3) units, and angle 100.02498786°
= ½*3sin(180-2asin(1/3)) + ½*2*√(44/3)sin100.02498786
= 0.94280904158 + 3.77123616635
= 4.71404520793 space units.
Therefore;
Area Blue ÷ Area Red is;
0.94280904158 ÷ 4.71404520793
= 0.2
= 1/5
