Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side length of the inscribed equilateral triangle ABD be x.
Calculating x.
(12√(2))² = (½√(3)x)² + ((12√(2))-½(12√(2)-x))²
It implies;
x = 3(√(26-√(2)) cm.
Therefore;
Area Yellow exactly in cm² is;
Area trapezoid with parallel sides (3√(26)-3√(2)) cm and (2√(26)-2√(2)) cm, and height ½(√(78)-√(6)) cm.
= ½*½(√(78)-√(6))*((3√(26)-3√(2))+(2√(26)-2√(2)))
= ¼(√(78)-√(6))(5√(26)-5√(2))
= 35√(3)-5√(39)
= 5(7√(3)-√(39)) square units.
