# Mathematically perfect Hexagon!

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.