Question

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?

Answer 1

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