Geometry Toolkit

Geometry

Naming by the number of sides

Any flat shape bounded by straight sides is a polygon, and its name comes from how many sides it has

Sides	Name
3	triangle
4	quadrilateral
5	pentagon
6	hexagon
8	octagon
10	decagon

The syllabus names these six, so a seven- or nine-sided figure is not required by name
A regular polygon has every side the same length and every angle the same size
An irregular polygon has sides or angles that differ, and the word "regular" in a question is never decorative

Eight regular polygons named by their number of sides: triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon and decagon — Source: Properties of 2D shapes by Save My Exams

Calculating the angles inside a polygon belongs to the angles topic; here the requirement is the vocabulary

Exam tip

The exterior angles of any polygon total 360°, whatever the number of sides, and each pair of interior and exterior angles sits on a straight line. For a regular polygon that makes the exterior angle 360 ÷ n the quicker route in, and the number of sides comes back as 360 ÷ exterior angle.

Worked example

Angles of a regular polygon

A regular polygon has 12 sides. Find its exterior angle and its interior angle.

Solution:

The exterior angles of any polygon add to 360°, however many sides it has
The polygon is regular, so all 12 exterior angles are equal
Exterior angle = 360 ÷ 12 = 30°
An interior angle and its exterior angle lie on a straight line, so they add to 180°
Interior angle = 180 − 30 = 150°
The longer route gives the same answer: (12 − 2) × 180 = 1800°, and 1800 ÷ 12 = 150°
The exterior route is one step rather than three, which is why it is worth doing first