Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
a² = 32-32cos120
a = 4√(3) units.
b = 2a
b = 8√(3) units.
c² =32-32cos150
c = 7.72740661031 units.
sin30 = d/4
d = 2 units.
sin60 = e/4
e = 2√(3) units.
tan15 = 2√(3)/f
f = (6+4√(3)) units.
g =f-(8√(3)-2)
g = (8-4√(3)) units.
It implies;
Area yellow rectangle is;
4*(8-4√(3))
= (32-16√(3)) square units.
Area yellow pentagon is;
2(area triangle with height 4 units and base 4sin120 units) + Area triangle with height 4√(3) units and base 4√(3)sin30 units.
= 2(½*4*4sin120) + ½*(4√(3))²*sin30
= (8√(3) + 12) cm².
Total Yellow Area in form of a-b√(3) square units is;
(32-16√(3)) + (8√(3) + 12)
= (44-8√(3)) square units.
