Mathematics Question and Solution
Calculating Shaded Blue Area.
Notice.
½(10) = 5 cm is the radius of the inscribed circle.
a² = 2(10)²
a = 10√(2) cm.
a is the diagonal of the ascribed square.
b = ½(a)
b = 5√(2) cm.
It implies;
10² = 5²+(5√(2))²-2*5*5√(2)cosc
100 = 25+50-50√(2)cosc
50√(2)cosc = 75-100
cosc = -(25)/(50√(2))
c = acos(-¼*√(2))
c = 110.704811055°
d = 2c
d = 221.409622109°
e = 360-d
e = 138.590377891°
(5/sinf) = (10/sin110.704811055)
f = 27.8855668363°
g = 2f
g = 55.7711336726°
Therefore, area shaded blue is;
2(area sector with radius 5 cm and angle 138.590377891°-area triangle with height 5 cm and base 5sin138.590377891-area sector with radius 10 cm and angle 55.7711336726°+area triangle with height 10 cm and base 10sin55.7711336726)
= 2(30.2357300723-8.26797284703-48.6694955078+41.3398642356)
= 2(14.6381259531)
= 29.2762519062 cm²
