Mathematics Question and Solution
Calculating radius of the inscribed circle.
a² = 4²+4²-2*4*4cos(90-30)
a² = 32-32cos60
a² = 16
a = 4 units.
Let b be the radius of the inscribed circle.
c = (4-b) units.
d = 60-45
d = 15°
e² = 2b²
e = √(2)b units.
Calculating b.
It implies;
cos15 = (0.5*4)/e
cos15 = 2/√(2)b
b = 2/(√(2)cos15)
b = 1.4641016151 units.
Again, b is the radius of the inscribed circle.
Therefore, area inscribed circle is;
πb²
= π(1.4641016151)²
= 6.7342977158 square units.
