Mathematics Question and Solution
Calculating Area Ascribed Regular Hexagon.
Let x be the side length of the ascribed regular hexagon.
a² = 2x²-2x²cos120
a = √(3)x units.
a is DF.
sin60 = b/x
b = ½√(3)x units.
sin30 = c/x
c = ½(x) units.
d = 2c+x
d = 2*½(x)+x
d = 2x units.
d is CF.
½*xesin30 = 2
xe = 8
e = (8/x) units.
½*xf = 5
xf = 10
f = (10/x) units.
Calculating x.
e+f = a
(8/x)+(10/x) = √(3)x
18 = √(3)x²
x = √(18/√(3))
x = 3.22370979547 units.
Recall.
b = ½√(3)x units.
And x = 3.22370979547 units.
b = 0.5√(3)*3.22370979547
b = 2.79181457731 units.
Again.
d = 2x units.
And x = 3.22370979547 units.
d = 2*3.22370979547
d = 6.44741959094 units.
Area ascribed regular hexagon is;
2*½(6.44741959094+3.22370979547)*2.79181457731
= (6.44741959094+3.22370979547)*2.79181457731
= 9.67112938641*2.79181457731
= 27 square units.
