Hexagon abcdef has has vertices a(-2,4), b(0,4), c(2,1), d(5,1), e(5,-2), f(-2,-2). sketch the figure on the coordinate plane. what is the area of the hexagon?

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle, which equals {\displaystyle {\tfrac {2}{\sqrt {3 {\displaystyle {\tfrac {2}{\sqrt {3 times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflection symmetries (six lines of symmetry