Mathematics Question and Solution
a² = 6²+2²
a =√(40)
a = 2√(10) units.
b = ½(a)
b = √(10) units.
c² = 6²+5²
c = √(61) units.
d = (atan(5/6)-atan(1/3))°
tan(atan(5/6)-atan(1/3)) = e/√(10)
e = 1.23741299746 units.
cos(atan(5/6)-atan(1/3))= √(10)/f
f = 3.39576072866 units.
Area Orange is;
½(6*5)-½(6*2)*½(√(10)*1.23741299746
= 15-6-1.95652173913
= 7.04347826087 square units.
Calculating Purple Area.
g = 90-atan(6/5)
g = 39.80557109227°
h = atan(√(10)/1.23741299746)
h = 68.62937773061°
j = 180-39.80557109227-68.62937773061
j = 71.56505117712°
k = √(61)-3.39576072866
k = 4.41448894725 units.
(4.41448894725/sin(71.56505117712)) = (l/sin(39.80557109227))
l = 2.9789572161 units.
Area Purple is;
0.5*2.9789572161*4.41448894725sin68.62937773061
= 6.12318840579 square units.
It implies;
Area Purple ÷ Area Orange exactly in decimal is;
6.12318840579÷7.04347826087
= 0.86934156378
≈ 0.87 to 2 decimal places.
