Mathematics Question and Solution
a = 6-2
a = 4 units.
b² = 6²-4²
b = 2√(5) units.
c = 6-b
c = (6-2√(5)) units.
d = asin(⅔)°
tan(asin⅔) = e/(6-2√(5))
e = ⅕(12√(5)-20) units.
f = 4+e
f = ⅕(12√(5)) units.
g² = 6²+(⅕(12√(5)))²
g = ⅕(18√(5)) units.
6² = (⅕(18√(5)))²+(⅕(12√(5)))²-2*⅕*⅕*18*12*5cosh
36 = ⅕(468)-⅕(432)cosh
⅕(432)cosh = ⅕(468)-36
⅕(432)cosh = ⅕(288)
h = acos(288/432)
h = 48.18968510422°
i = 90-h
i = 41.81031489578°
Therefore;
Area Shaded in square units to 2 decimal places is;
½*(6-2√(5))*⅕(12√(5)-20) + ½*6*⅕(12√(5)) - (41.81031489578*36π/360)
= 1.043961348 + 16.099689438 - 13.13509781209
= 4.00855297391 square units.
≈ 4.01 square units.
