Mathematics Question and Solution
Calculating blue area (area inscribed half circle).
15² = 13²+14²-2*13*14cosa
364cosa = 140
a = 67.380135052°
(15/sin67.380135052) = (13/sinb)
b = 53.1301023542°
c = 180-a-b
c = 59.4897625938°
Let d be the radius of the inscribed blue half circle.
Calculating d.
sin59.4897625938 = d/e
e = 1.1607142857d units.
sin53.1301023542 = d/f
f = 1.25d
Notice.
e+f = 15
1.1607142857d+1.25d = 15
2.4107142857d = 15
d = 6.2222222223 units.
d = 56/9 units.
It implies, area blue inscribed half circle is;
½(πd²)
= ½*((56*56)/(9*9))π
= (1568π/81) square units.
= 6.1618506362 square units.
