What is the area of equiangular hexagon?

Answer 1

A regular hexagon, one that is both equiangular and equilateral, has an area of 3 times the square root of three times the square of the side length, all divided by 2. Once the side length has been discovered, the area can easily be calculated. However, hexagons with irregular bounds can have their area found, if their vertices are known by coordinate. Multiply each vertex's x coordinate by the y coordinate of the next vertex (looping back around to the first for the sixth), taking the sum of the six numbers found. Then multiply each vertex's y coordinate by the next's x coordinate, once again summing up these six numbers. Finally, subtract the larger of the two by the smaller, and divide this number by 2. This will provide the area in the units of the plot used to find the coordinates.