Mathematics Question and Solution
Let the regular triangle side length be 1 unit.
Calculating Area Purple.
(1/sin105) = (a/sin60)
a = 0.8965754722 units.
Area Purple is;
0.5*0.8965754722*1sin45 - ½*½*½
= 0.3169872981-0.125
= 0.1919872981 square units.
Calculate Green Area.
sin60 = b/1
b = √(3)/2 units.
((√(3)/2)/sin135) = (0.5/sinc)
c = 24.0948425521°
d = 180-135-24.0948425521
d = 20.9051574479°
(0.5/sin24.0948425521) = (e/sin20.9051574479)
e = 0.4370160244 units.
Where e is the diagonal of green area.
Area Green is;
½(0.4370160244)²
= 0.0954915028 square units.
It implies;
Area Green ÷ Area Purple exactly in decimal is;
0.0954915028÷0.1919872981
= 0.4973844819
≈ 0.50 to 2 decimal places.
