Mathematico | Mathematico

The six vertices of a regular hexagon lie upon the circumference of the circle

x^{2} + y^{2} - 6 x + 4 y - 37 = 0

Find the area of the hexagon.

Complete the square on $x^{2} - 6 x$ and on $y^{2} + 4 y$ to get the equation of the circle in the form

(x - a)^{2} + (y - b)^{2} = r^{2}

You need $r$ ( $a$ and $b$ are irrelevant).

Inscribed hexagon

The angle $θ$ should be easy to find, since the hexagon is formed by $6$ identical triangles.