Polygons

Understanding Polygons

  • Polygons are two-dimensional shapes with straight sides. They are a core component of many geometry and measure concepts.
  • The term ‘polygon’ means ‘many angles’, which refers to the joints where the straight lines meet.
  • A polygon is regular if all its sides and interior angles are equal. An example of a regular polygon is an equilateral triangle.

Categories of Polygons

  • Triangular Polygon: The simplest form of a polygon is the triangle, which has three sides and three angles.
  • Quadrilateral Polygon: Quadrilaterals have four sides and four angles. Examples of quadrilaterals include squares, rectangles and parallelograms.
  • Pentagonal Polygon: Pentagons have five sides and five angles.
  • Hexagonal Polygon: Hexagons are polygons with six sides and six angles.

Polygon Vertices and Sides

  • The corners of the polygon are known as vertices.
  • The straight lines that form a polygon and meet at the vertices are called sides.
  • The sum of the interior angles in any polygon is dependent on the number of sides in the polygon. This sum can be calculated using the formula (n-2) x 180, where n is the number of sides.

Polygon Perimeters

  • The perimeter of a polygon is the total length around its edge. It can be calculated by adding all the lengths of the sides together.

Central and Interior Angles

  • The central angle of a regular polygon is the angle at the centre of the polygon formed between two adjacent vertices. It can calculated by dividing 360 by the number of sides.
  • The interior angle of a regular polygon can be calculated using the formula 180(n-2) / n, where n is the number of sides.

Area of Regular Polygons

  • The area of regular polygons can be calculated using different formulas depending on the specific polygon. For example, the area of a rectangle is length x width, and the area of an equal-sided triangle is 1/2 x base x height.

Recall these points about polygons when revising to form a comprehensive understanding of these fundamental geometric shapes. Keep practicing to increase familiarity with the properties, measurements and formulas related to polygons.