The hexagon is made up of 6 equilateral triangles built inside a 100x100 unit grid. Since we know that the teal line is 50 units long, we know that all sides of the triangle are also 50 units long. We need to know the height of a single triangle; for example the blue line .
Remember the
Pythagorean theorem
(a
2
+ b
2
= c
2
). With it, we now know enough to calculate the length of that
blue line (
b
)
:
25
2
+ b
2
= 50
2
. Solving that equation for
b
gives us
b = 43.30
; or
b = √1875
if you want to be precise. We can now calculate the position of each of the
6 points
of the hexagon.