Mathematics Question and Solution
Calculating green area.
a² = 2²+2²
a = √(8)
a = 2√(2) units.
sin30 = b/a
½ = b/(2√(2))
b = √(2) units.
c²+b² = a²
c²+√(2)² = (2√(2))²
c² = 8-2
c = √(6) units.
Area green is;
(½*2*2)+(½*√(2)*√(6))
= (2+√(3)) square units.
= 3.7320508076 square units.
Calculating yellow area.
d = -45+60
d = 15°
tan15 = b/e
e = (√(2)/tan15) units.
e = 5.2779168675 units.
sin15 = √(2)/f
f = (√(2)/sin15) units.
f = 5.4641016151 units.
2g² = f²
2g² = 29.8564064601
g = √(29.8564064601/2)
g = 3.8637033051 units.
Area yellow is;
(0.5*√(2)*5.2779168675)+(0.5*3.8637033051*3.8637033051)
= 3.7320508075+7.464101615
= 11.1961524225 square units.
= 3(2+√(3)) square units.
Therefore;
C ÷ D
Or
Area Yellow ÷ Area Green
= 11.1961524225÷3.7320508076
= 3
Or
= 3(2+√(3))÷(2+√(3))
= 3
