Mathematics Question and Solution
Let a be the side length of the regular hexagon.
Calculating a.
(14/sin60) = (16/sinb)
b = 81.7867892983°
c = 180-60-b
c = 38.2132107017°
It implies;
(a/sin38.2132107017) = (14/sin60)
a = 10 units.
Again, a is the side length of the regular hexagon.
sin30 = d/a
d = 10sin30
d = 5 units.
e = 2d+a
e = 2(5)+10
e = 20 units.
f = e-16
f = 4 units.
It implies;
(4/sin81.7867892983) = (g/sin38.2132107017)
g = 2.5 units.
Therefore the required area, area pink is;
Area triangle with height 4 units and base 2.5sin60 units.
= 0.5*4*2.5sin60
= 5sin60
= ½(5√(3)) square units.
= 2.5√(3) square units.
= 4.3301270189 square units.
