Mathematics Question and Solution
Calculating the blue and circle area.
Notice.
The circle is centralized inscribing the ascribed square.
a² = 12²+4²
a = √(144+16)
a = √(160)
a = 4√(10) units.
b² = 12²+12²
b = √(2*12²)
b = 12√(2) units.
b is the diagonal of the ascribed square.
c = ½(b)
c = 6√(2) units.
tand = 4/12
d = atan(1/3)°
e = ½(90)-d
e = (45-atan(1/3))°
e = 26.5650511771°
sine = f/c
sin26.5650511771 = f/(6√(2))
f = 3.7947331922 units.
f is the radius of the inscribed circle.
Therefore, area Inscribed circle is;
πf²
= π(3.7947331922)²
= 14.4π square units.
= ⅕(72π) square units.
g²+3.7947331922² = (6√(2))²
g² = 72-14.4
g = √(57.6)
g = ⅕(12√(10)) units.
g = 7.5894663844 units.
h = a-g
h = 4√(10)- ⅕(12√(10))
h = ⅕(8√(10)) units
tanj = 12/4
j = atan(3)°
tank = (3.7947331922)/(⅕(8√(10)))
k = 36.8698976458°
l = 2k
l = 73.7397952917°
m = 180-j-l
m = 180-atan(3)-73.7397952917
m = 34.6951535312°
n = 12-4
n = 8 units.
n is the height of the blue area.
tan34.6951535312 = o/8
o = 8tan34.6951535312
o = 5.53846153845 units.
o is the base of the blue area.
Area blue is;
½(on)
= 0.5*5.53846153845*8
= 22.1538461538 square units.
Therefore;
Area circle is;
⅕(72π) square units.
Area blue is;
22.1538461538 square units.
