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.