Mathematics Question and Solution
Calculating x.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the green regular hexagon.
b = ½(x) units.
c = ⅙(x) units.
It implies;
d ~ b
b ~ c
Therefore;
d ~ ½(x)
½(x) ~ ⅙(x)
Cross Multiply (Calculating d).
⅙(dx) = ¼(x²)
2d = 3x
d = ½(3x) units.
Calculating x, the side length of the green regular hexagon.
13² = d²+b²-2dbcos120
169 = ¼(9x²)+¼(x²)-2*½(3x)*½(x)cos120
169 = ¼(9x²)+¼(x²)+¼(3x²)
676 = 9x²+x²+3x²
13x² = 676
x² = 13*4
x = 2√(13) units.
Again, x is the side length of the green regular hexagon.
