# Polygons

## Polygons

- A polygon is a 2D shape formed by straight lines.
- Polygons can be classified based on both their sides and angles.
- They can be divided into two general categories: regular or irregular.
- A regular polygon has all sides and angles equal. Examples include squares, regular hexagons, and equilateral triangles.
- On the other hand, an irregular polygon does not have all its sides and angles equal, such as a scalene triangle or an irregular quadrilateral.
- The sum of interior angles of a polygon can be calculated using the formula (n-2)x180°, where n represents the number of sides.
- The exterior angles of any polygon, regular or irregular, always add up to 360°.
- In a regular polygon, each individual exterior angle can be found by dividing 360° by the number of sides.
- Key properties of some specific types of polygons include:
- Triangle: The sum of all angles is 180°. It can be equilateral (all sides and angles equal), isosceles (two sides and angles equal), or scalene (no sides or angles equal).
- Quadrilateral: The sum of all angles is 360°. It can be square, rectangle, parallelogram, trapezium, rhombus, or kite.
- Pentagon: A regular pentagon has each internal angle as 108°.
- Hexagon: A regular hexagon has each internal angle as 120°.

- The segment, arc, and sector are parts of a circle, which isn’t a polygon but is an important area of study within geometry and measures.
- Perimeter and area are important features of polygons. The perimeter is the length around the outside, while area is the space inside a polygon.
- While the perimeter can usually be found by simply adding up the lengths of the sides, area calculations can be more complex and often require specific formulae.
- Key area formulae include: Triangle = 1/2bh (base x height), Rectangle = bh, Square = s² (side length squared), Parallelogram = bh, Trapezium = 1/2(a+b)h (average of parallel sides x height), Circle = πr² (pi x radius squared), and sectors or segments of a circle often involve fractions or ratios of these.