Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the small square be 1 unit.
Therefore;
Area large square is;
((1/tan15)-1)²
= 7.46410161514 square units.
Area orange is;
Area large square - area triangle with height 2.73205080757 units and base 0.73205080757 units - area triangle with height 2 units and base 0.53589838486 units - area triangle with height 2.19615242271 units and base 0.58845726812 units.
= 7.46410161514 - ½(2.73205080757*0.73205080757) - ½(2*0.53589838486) - ½(2.19615242271*0.58845726812)
= 7.46410161514 - 1 - 0.53589838486 - 0.64617092752
= 5.28203230278 square units.
It implies;
Area Orange ÷ Area Large Square in its simplest decimal form is;
5.28203230278 ÷ 7.46410161514
= 0.70765814496
