MathematicsExam code: 0580
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
- The angles topic covers polygon angle calculations in full; the example below shows the quickest route for a regular polygon
Worked example
Angles of a regular polygon
A regular polygon has 24 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 24 exterior angles are equal
- Exterior angle = 360 ÷ 24 = 15°
- An interior angle and its exterior angle lie on a straight line, so they add to 180°
- Interior angle = 180 − 15 = 165°
- The longer route gives the same answer: (24 − 2) × 180 = 3960°, and 3960 ÷ 24 = 165°
- The exterior route is a division and a subtraction, while the angle-sum route needs three operations, which is why it is worth doing first