Mathematics Question and Solution
a = 10√(2) units.
a is a diagonal of the square.
(12/sin45) = (10√(2)/sinb)
b = 56.44269023808°
tan56.44269023808 =10/c
c = 6.63324958071 units.
d = 10-6.63324958071
d = 3.36675041929 units.
d is adjacent length (base) of the blue inscribed right-angled triangle.
e = 90-56.44269023808
e = 33.55730976192°
f = 90-33.55730976192-45
e = 11.44269023808°
tan11.44269023808 = f/10
f = 2.02410864032 units.
g = 10-2.02410864032
g = 7.97589135968 units.
g is adjacent length (height) of the blue inscribed right-angled triangle.
Therefore, area blue is;
½*d*g
= 0.5*3.36675041929*7.97589135968
= 13.42641778971 square units.
