Mathematics Question and Solution
Calculating Area Pink Regular Hexagon.
Let a be the side length of the pink regular hexagon.
Let b be the side length of the red regular hexagon with area 6 square units.
A nice analysis of the composite plane shape implies that;
c = a+b
Where c is the side length of the yellow regular hexagon.
Notice.
120° is each of the interior angle of the regular hexagons.
Calculating b.
c² = 2b²-2b²cos120
c² = 3b²
c = √(3b²)
c = √(3)b units.
c is the height of the red regular hexagon.
It implies;
(2*½*b*bsin120)+(√(3)b*b)= 6
½√(3)b²+√(3)b² = 6
½(3√(3)b²) = 6
3√(3)b² = 12
√(3)b² = 4
b² = 4/√(3)
b = √(4/√(3)) units.
b = 1.5196713713 units.
Again, b is the side length of the red regular hexagon.
Calculating a.
sin30 = b/a
½ = 1.5196713713/a
a = 2*1.5196713713
a = 3.0393427426 units.
Again, a is the side length of the pink regular hexagon.
d² = 2(3.0393427426)²-2(3.0393427426)²cos120
d = 5.2642960518 units.
d is the height of the pink regular hexagon.
Therefore, area pink regular hexagon is;
½(2*3.0393427426²sin120)+(5.2642960518*3.0393427426)
= 8+16
= 24 square units.
