Polygons
Maths: Edexcel IGCSE Higher, topic 4.2.1
Regular Polygons
A regular polygon is a many sided shape where all the sides are the same length and all the angles are the same size. The order of rotation and the number of lines of symmetry of a regular polygon are the same as the number of sides.
Equilateral triangle (3 sides)
Square (4 sides)
Pentagon (5 sides)
Hexagon (6 sides)
Heptagon (7 sides)
Octagon (8 sides)
Decagon (10 sides)
Angles in a Polygon
The interior (inside) angles of a polygon (a shape made of straight lines) are the angles inside the shape.
Interior (inside) angles
- The sum of the interior angles is (n - 2) × 180° where n is the number of sides the polygon has.
Exterior angles
- If you extend the side of a polygon outside the shape then the exterior angle is the angle between the extended line and the adjacent edge.
- The exterior angles add up to 360°.
- In a regular polygon the exterior angle + interior angle = 180°.
Test yourself on Polygons
What do we call a shape with 6 sides all the same length?
Which of these describes a square?
What do the exterior angles of a triangle add up to?
What is the sum of the exterior angles of this regular pentagon?
What type of angles are being shown here?