Mathematics Question and Solution
cosa = ½
a = acos(½)°
a = 60°
Calculating Red Perimeter.
It is;
2(length of arc of a sector with radius 2 units and angle acos(½)°).
= 2(acos(½)π*2*2/360)
= 4.1887902048 units.
Calculating Green Area.
It is;
2(half perimeter red - area triangle with height 2 units and base 2sin(acos(½)) units.)
= 2(½*4.1887902048-½*2*2sin(acos(0.5)))
= 2(2.0943951024-1.7320508076)
= 0.7246885897 square units.
Therefore;
Red Perimeter ÷ Green Area is;
= 4.1887902048÷0.7246885897
= 5.7801244078
= 5.78 to 2 decimal places.
Or
Red length is;
2(60π*2*2/360)
= ⅓(4π) units.
Green Area is;
2((60π*2*2÷360)-(0.5*2*2sin60))
= 2((2π/3)-√(3))
= ((4π/3)-2√(3)) square units.
Therefore;
Red Perimeter ÷ Green Area is;
⅓(4π) ÷ ((4π/3)-2√(3))
= 4.1887902048÷0.7246885896
= 5.7801244074
= 5.78 to 2 decimal places.
