Mathematics Question and Solution
Notice!
The composite plane shape consist of two congruent quarter circles with radius 2 units each.
a = 3-2
a = 1 unit.
cosb = 1/2
b = acos(½)°
b = 60°
Area green is;
2(area sector with radius 2 units and angle 60° - area triangle with height 2 units and base 2sin(60) units).
= 2((60π*2*2÷360)-(0.5*2*2sin(60)))
= 2(⅔(π)-√(3))
= ⅔(2π-3√(3)) square units.
Perimeter red is;
2(length of arc with radius 2 units and angle 60°)
= 2(60π*2*2÷360)
= ⅔(2π) units.
Therefore;
Red Perimeter ÷ Green Area is;
⅔(2π)÷⅔(2π-3√(3))
= 2π÷(2π-3√(3)) per unit.
= 5.7801244074 per unit.
