Mathematics Question and Solution
Calculating area blue isosceles triangle.
(10/sin45) = (6/sina)
a = 25.1040902502°
b = 180-45-25.1040902502
b = 109.89590975°
c = 180-109.89590975
c = 70.10409025°
Let r be the radius of the half circle.
d = (r-6) units.
Calculating r.
r² = 10²+(r-6)²-2*10(r-6)cos70.10409025
r² = 100+r²-12r+36-6.80624847494r+40.8374908496
18.80624847494r = 136+40.8374908496
18.80624847494r = 176.83749085
r = 176.83749085/18.80624847494
r = 9.40312423744 units.
e = 2r-6
e = 2*9.40312423744-6
e = 12.8062484749 units
e is the base of the blue shaded isosceles triangle.
tan70.10409025 = f/(0.5*12.8062484749)
f = (0.5*12.8062484749)tan70.10409025
f = 17.6923816208 units.
f is the height of the blue shaded isosceles triangle.
Area blue shaded isosceles triangle is;
½*e*f
= 0.5*12.8062484749*17.6923816208
= 113.286517574 square units.
