Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side length of the square be a.
tanb = a/(0.5a)
b = atan(2)°
c = 180-b-45
c = (135-atan(2))°
(0.5a/sin(135-atan(2)) = (d/sin45)
d = 0.3726779962a cm.
cos(atan(0.5)) = 0.5a/e
e = 0.5590169944a cm.
Therefore;
Calculating a.
0.5*0.3726779962a*0.5590169944a = 10
0.1041666667a² = 10
a² = 96
a = 4√(6) cm.
Again, a is the side length of ascribed square.
tan(atan(½)) = f/(2√(6))
f = √(6) cm.
g = 4√(6)-g
g = 3√(6) cm.
(4√(6)/sin(135-ata(¾))) = (h/sin(45))
h = 6.9985421222 cm.
(4√(6)/sin(135-ata(¾))) = (j/sin(atan(3/4)))
j = 5.9384599117 cm.
Area purple exactly in decimal is:
0.5*3√(6)*5.9384599117sin45
= 15.4285714286 cm²
