# 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.