Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the square be 2 units.
Area square is;
2² = 4 square units.
Calculating green area.
It will be;
Area square of side 2 units - area triangle of two equal lengths ⅔(√(3)) units and angle 120°, the angle they form - area triangle of lengths (4-2√(3)) units and 2 units, and angle 60°, the angle they form.
It implies;
4 - ½(⅔(√(3)))²sin120 - ½*2(4-2√(3))sin60
= 4 - ⅓√(3) - (2√(3)-3)
= 4 - ⅓√(3) -2√(3) + 3
= 7 - ⅓(7√(3))
= ⅓(21-7√(3)) square units.
Therefore;
Area Green ÷ Area Square in its simplest form is;
⅓(21-7√(3)) ÷ 4
= (21-7√(3))/12
=7(3-√(3))/12
