Names and types
- A polygon is a flat shape with straight sides: triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9) and decagon (10).
- A regular polygon has all its sides equal and all its angles equal.
Interior angles
- The interior angles of a polygon with n sides add up to (n − 2) × 180°.
- A hexagon's angles add up to 4 × 180 = 720°. Each angle of a regular hexagon is 720 ÷ 6 = 120°.
Exterior angles
- The exterior angles of any polygon add up to 360°.
- Each exterior angle of a regular polygon is 360° ÷ n. The interior and exterior angles at a corner add up to 180°.
- To find the number of sides of a regular polygon, work out n = 360 ÷ exterior angle. An interior angle of 144° means an exterior angle of 36°, so n = 10.
Quadrilaterals
- A parallelogram has opposite sides parallel and equal, and opposite angles equal. A rhombus is a parallelogram with four equal sides.
- A trapezium has exactly one pair of parallel sides. A kite has two pairs of equal sides next to each other.
Key terms
- Polygon
- A flat shape with straight sides.
- Regular polygon
- A polygon with all sides equal and all angles equal.
- Interior angle
- An angle inside a polygon at one of its corners.
- Exterior angle
- The angle between one side of a polygon and the next side extended.
- Pentagon
- A polygon with 5 sides.
- Hexagon
- A polygon with 6 sides.
- Octagon
- A polygon with 8 sides.
- Trapezium
- A quadrilateral with exactly one pair of parallel sides.