Mathematics Question and Solution
Let a be the radius of the quarter circle.
It implies;
a² = a²+4²-2*a*4cosb
8cosb = 16
acosb = 2
cosb = 2/a --- (1).
8² = a²+4²+2*a*4cosb
64 = a²+16+8acosb
48 = a²+8acosb --- (2).
Substituting (1) in (2) to get a, radius of the quarter circle.
48 = a²+8a(2/a)
48 = a²+16
a² = 48-16
a² = 32
a = √(32)
a = 4√(2) units.
Again, a is the radius of the quarter circle.
Therefore, area blue (area quarter circle) is;
¼(4√(2))²π
= ¼*4*4*2π
= 8π square units.
