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.

If you know the coordinates of the vertices of the polygon, there are two methods:

- A manual method. See Area of a polygon (Coordinate geometry).
- A computer algorithm. See Algorithm to find the area of any polygon

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.
The examples below give you some basic approaches to try.

Here, the irregular hexagon is divided in to 4 triangles by the addition of the red lines. (See Area of a Triangle)

We know how to find the area of a regular polygon so we just subtract the area of the 'missing' triangle created by drawing the red line. (See Area of a Regular Polygon and Area of a Triangle.)

We know how to find the area of a parallelogram so we just find the area of each one and add them together. (See Area of a Parallelogram).

As you can see, there an infinite number of ways to break down the shape into pieces that are easier to manage. You then add or subtract the areas of the pieces. Exactly how you do it comes down to personal preference and what you are given to start.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Trapezium
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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