Mathematics Question and Solution
Let the square side be a.
a² = πr²
And r = 1 unit, π = 22/7
a² = (22/7)
a = √(22/7) units.
b = ½(a)
b = ½√(22/7) units.
c² = 2a²
c² = 2√(22/7)²
c = √(44/7)
c = ⅐(2√(77)) units.
c is the diagonal of the square.
cosd = ½√(22/7)/1
d = acos(½√(22/7))°
d = 27.5750477105°
e = 45-d
e = 17.4249522895°
f = 3e
f = 34.849904579°
f is the required angle, phi.
g² = 2-2cos34.849904579
g = 0.5989126703 units.
2h² = 0.5989126703²
h = 0.4234952105 units.
Shaded Area is;
0.5(0.4234952105)²+(0.5*sin34.849904579)-(34.849904579π/360)
= 0.0896740967+0.2857142857-0.3041227895
= 0.0712655929 square units.
