Mathematics Question and Solution
Let the side of the equilateral triangle be 2 units.
Let the side of the square be a.
Calculating a.
tan60 = a/1
a = √(3) units.
Area square is;
a²
= √(3)²
= 3 square units.
Calculating area green.
b² = 2√(3)²
b = √(6) units.
c = 180-60-45
c = 75°
(√(3)/sin75) = (d/sin60)
d = 1.55291427062 units.
e = b-d
e = 0.89657547217 units.
(f/sin45) = (√(3)/sin75)
f = 1.26794919243 units.
(1.26794919243/sin45) = (0.89657547217/sing)
g = 30°
sin30 = h/(√(3)+1)
h = ½(√(3)+1) units.
Therefore,
Area green is;
½*½(√(3)+1)(√(3)+1)sin(60) - ½*√(3)*0.89657547217sin45
= 1.61602540378 - 0.54903810568
= 1.0669872981 units.
Therefore;
Area Green ÷ Area Square exactly in decimal is;
1.0669872981 ÷ 3
= 0.3556624327
= 5585697/15705052 exactly.
