Card 6 of 8
2D shapes
Polygon angles, triangles, quadrilaterals, area and perimeter formulas.
| Polygon | Sides | Interior angles add to | Each interior angle* | Each exterior angle* | Lines of symmetry* |
|---|---|---|---|---|---|
| Triangle | 3 | 180° | 60° | 120° | 3 |
| Quadrilateral | 4 | 360° | 90° | 90° | 4 |
| Pentagon | 5 | 540° | 108° | 72° | 5 |
| Hexagon | 6 | 720° | 120° | 60° | 6 |
| Heptagon | 7 | 900° | 128.6° | 51.4° | 7 |
| Octagon | 8 | 1080° | 135° | 45° | 8 |
| Nonagon | 9 | 1260° | 140° | 40° | 9 |
| Decagon | 10 | 1440° | 144° | 36° | 10 |
| Dodecagon | 12 | 1800° | 150° | 30° | 12 |
* when the polygon is regular (all sides and angles equal)
The formula, so you never need the table: interior angles add to (n − 2) × 180°. Divide by n for each angle in a regular polygon. The shortcut: exterior angles of ANY polygon always add to 360°. So each exterior angle of a regular n-gon is 360 ÷ n, and interior = 180 − exterior. This is usually the faster route.
Triangles
| Type | Sides | Angles |
|---|---|---|
| Equilateral | 3 equal | all 60° |
| Isosceles | 2 equal | 2 equal |
| Scalene | all different | all different |
| Right-angled | — | one 90° |
Quadrilaterals
| Shape | Key properties |
|---|---|
| Square | 4 equal sides, 4 right angles, 4 lines of symmetry, diagonals equal & perpendicular |
| Rectangle | opposite sides equal, 4 right angles, 2 lines of symmetry |
| Rhombus | 4 equal sides, opposite angles equal, 2 lines of symmetry |
| Parallelogram | opposite sides parallel & equal, 0 lines of symmetry |
| Trapezium | exactly one pair of parallel sides |
| Kite | 2 pairs of adjacent equal sides, 1 line of symmetry |
The parallelogram having zero lines of symmetry surprises nearly every child. It has rotational symmetry of order 2, which is a different thing.
Area and perimeter
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | length × width | 2(l + w) |
| Square | side² | 4 × side |
| Triangle | ½ × base × height | add the three sides |
| Parallelogram | base × height | 2(a + b) |
| Trapezium | ½ × (a + b) × height | add the four sides |
| Circle | π r² | 2π r (circumference) |