The formulae below give the area of a regular polygon. Use the one that matches what you are given to start. They assume you know how many sides the polygon has. Most require a certain knowledge of trigonometry.
S is the length of any side
N is the number of sides
TAN is the tangent function calculated in degrees
Note: Unlike a regular polygon, unless you know the coordinates of the vertices, there is no easy formula for the area of an irregular polygon. Each side could be a different length, and each interior angle could be different. It could also be either convex or concave.
One approach is to break the shape up into pieces that you can solve - usually triangles, since there are many ways to calculate the area of triangles. Exactly how you do it depends on what you are given to start. Since this is highly variable there is no easy rule for how to do it.