Mathematics Question and Solution
Calculating Perimeter of the ascribed Hexagon.
a = ⅙*180(6-2)
a = 120°
Let x be the side length of the regular hexagon.
b² = 2x²-2x²cos120
b = √(3)x units.
sin30 = c/x
c = ½(x) units.
d = x+2c
d = 2x units.
e = d-11
e = (2x-11) units.
f = ½(a)
f = 60°
Calculating x.
7² = x²+(2x-11)²-2x(2x-11)cos60
49 = x²+4x²-44x+121-2x²+11x
49 = 3x²-44x+121+11x
3x²-33x+72 = 0
x²-11x+24 = 0
x²-8x-3x+24 = 0
x(x-8)-3(x-8) = 0
(x-8)(x-3) = 0
It implies;
x ≠ 3 units.
x = 8 units.
Again, x is the side length of the ascribed regular hexagon.
Therefore, regular hexagon perimeter p is;
p = 6(x)
p = 6*8
p = 48 units.
