Mathematics Question and Solution
tan30 = a/12
a = 12tan30
a = 4√(3) cm.
a is the side length of the square.
b = ½(12)+a
b = (6+4√(3)) cm.
c = ½(a)
c = 2√(3) cm.
Observing similar right-angled triangle side length ratios.
2√(3) - d
(6+4√(3)) - 4√(3)
Cross Multiply.
24 = d(6+4√(3))
d = 12/(3+2√(3))
d = 12(3-2√(3))/(-3)
d = 4(2√(3)-3) cm.
Shaded Area exactly is;
Area square with side 4√(3) cm - Area triangle with height 4√(3) cm and base 4(2√(3)-3) cm.
= (4√(3))²-½*4(2√(3)-3)*4√(3)
= 48-48+24√(3)
= 24√(3) cm²
