Mathematics Question and Solution
Calculating AB.
Notice.
1 unit is the side length of each of the composite plane shape.
a = ½*180(6-2)
a = 120°
a is the single interior angle of the regular hexagon.
b = 180(12-2)/12
b = 150°
b is the single interior angle of the regular polygon with 12 sides.
sin30 = c/1
c = 0.5 units.
sin60 = d/1
d = ½√(3) units.
sin30 = e/1
e = 0.5 units.
Therefore, length AB is;
AB = 2c+1+3d+1+e
AB = 2(0.5)+1+3(½√(3))+1+0.5
AB = 3.5+0.5(3√(3))
AB = ½(7)+½(3√(3))
AB = ½(7+3√(3)) units.
AB = 6.0980762114 units.
