A six-sided shape is called a hexagon as long as all six sides are straight lines and the lines connect to make one closed shape. If it does not close or has curved lines, there is no generic name for the shape.
A regular hexagon has six equal sides with six equal angles of 120 degrees between each side. The formula for the area of a regular hexagon is approximately 2.598 * s * s where s is the length of each side. All other hexagons are irregular. A hexagon is convex if it has no angles that point inwards which also means it has no interior angles greater than 180 degrees. It is concave if there is an interior angle greater than 180 degrees.