Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the small inscribed square side length be x.
The big inscribed square side length will be 2x.
Calculating x.
⅓(√(3)x+2√(3)x+3x+6x) = 18+6√(3)
(9+3√(3))x = 3(18+6√(3))
(3+√(3))x = 6(3+√(3))
x = 6 cm.
Therefore:
Area Blue exactly in decimal is;
Area triangle with height 12sin(atan(12/(12+4√(3))))÷sin(180-atan(12/(12+4√(3)))-atan(⅔)) cm and base 12sin(atan(⅔)) cm.
= ½*12sin(atan(12/(12+4√(3))))÷sin(180-atan(12/(12+4√(3)))-atan(⅔))*12sin(atan(⅔))
= 72sin(atan(12/(12+4√(3))))*sin(atan(⅔))÷(sin(180-atan(12/(12+4√(3)))-atan(⅔))
= 23.3967516537 cm²
