Mathematics Question and Solution
Calculating Area Blue.
a² = 2(12)²
a = 12√(2) units.
a is the diagonal of the square.
b = ½(a)
b = 6√(2) units.
tanc = 4/12
c = atan(⅓)°
d = 45-c
d = (45-atan(⅓))°
d = 26.5650511771°
e² = 12²+4²
e = √(12²+4²)
e = 12.6491106407 units.
sin26.5650511771 = r/(6√(2))
r = 3.7947331922 units.
r is the radius of the inscribed circle.
cos26.5650511771 = f/(6√(2))
f = 7.5894663844 units.
g = e-f
g = 12.6491106407-7.5894663844
g = 5.0596442563 units.
tanh = (12/4)
h = atan(3)°
h = 71.5650511771°
tanj = r/g
j = atan(3.7947331922/5.0596442563)
j = 36.8698976457°
k = 2j
k = 2(36.8698976457)
k = 73.7397952913°
It implies;
h+k+l = 180
l = 180-71.565051171-73.7397952913
l = 34.6951535377°
m = 12-4
m = 8 units.
tan34.6951535377 = n/8
n = 5.5384615398 units.
Therefore, area blue is;
½*8*n
= 4*5.5384615398
= 22.1538461592 square units.
