Mathematics Question and Solution
Let the side length of the three congruent squares be 1 unit.
Area Orange is;
1²
= 1 square units.
Calculating Area Blue.
a² = 1+2²
a = √(5) units.
⅓ = b/1
b = ⅓ units.
c = 1+⅓
c = (4/3) units.
cos(tan(½)) = d/(4/3)
d = (8√(5)/15) units.
d = 1.192569588 units.
e = √(5)-(8√(5)/15)
e = (7√(5)/15) units.
e = 1.0434983895 units.
cos(atan(½)) = (7√(5)/15)/f
f = (7/6) units.
tan(atan(½)) = g/(7√(5)/15)
½ = g/(7√(5)/15)
g = ½(7√(5)/15) units.
h = atan(½)°
½ = (⅓)/j
j = (⅔) units.
k = 1-j
k = 1-(2/3)
k = (⅓) units.
½ = l/(⅓)
l = (⅙) units.
m = 1+(⅙)
m = (7/6) units.
Area Blue is;
(½*(7/6)*√(5)sin(atan(½))) - (½*½*1) - (½*⅓*⅙)
= (7/12)-¼-(1/36)
= (5/9)-¼
= (11/36) square units.
It implies;
Area Blue ÷ Area Orange exactly is;
(11/36) ÷ 1
= 11/36
