Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Red ÷ Area Square Exactly.
Let the single side length of the square be 2 units.
Therefore;
Area square is;
2 x 2
= 4 square units.
Calculating Red Area.
It will be;
½(area square with single side length 2 units) - Area triangle with base 2(2-√(3)) units and height 2 units - Area sector with radius 2 units and angle 30°.
= ½(4) - ½(2*2(2-√(3)) - (4π/12)
= 2 - 4 + 2√(3) - (π/3)
= ⅓(6-12+6√(3)-π)
= ⅓(6√(3)-6-π)
= (42√(3)-42-22)/21
= (42√(3)-64)/21 square units.
Therefore;
Area Red ÷ Area Square is;
((42√(3)-64)/21)÷4
= (42√(3)-64)/84
= (21√(3)-32)/42
