📐 2D & 3D Shapes
🔄 Rotational Symmetry Order: Number of positions a shape looks the same in a full 360° turn.
🟦 2D Shapes
| Shape | Image | Vertices | Sides | Total Angle | Individual Angles | Lines of Symmetry | Rotational Symmetry | Area Formula | Perimeter |
|---|---|---|---|---|---|---|---|---|---|
| Square |  |
4 | 4 | 360° | 4 × 90° | 4 | Order 4 | a² | 4a |
| Rectangle |  |
4 | 4 | 360° | 4 × 90° | 2 | Order 2 | l × w | 2(l + w) |
| Circle |  |
0 | 0 | 0 | 0 | Infinite | Infinite | πr² | 2πr |
| Equilateral Triangle |  |
3 | 3 | 180° | 3 × 60° | 3 | Order 3 | (√3 / 4) × a² | 3a |
| Isosceles Triangle |  |
3 | 3 | 180° | Varies | 1 | Order 1 | ½ × base × height | a + 2b |
| Scalene Triangle |  |
3 | 3 | 180° | All different | 0 | Order 1 | ½ × base × height | a + b + c |
| Right Triangle |  |
3 | 3 | 180° | One 90°, two acute | None | Order 1 | ½ × base × height | a + b + c |
| Pentagon (Regular) |  |
5 | 5 | 540° | 5 × 108° | 5 | Order 5 | (5/4) × a² × cot(π/5) | 5a |
| Hexagon (Regular) |  |
6 | 6 | 720° | 6 × 120° | 6 | Order 6 | (3√3 / 2) × a² | 6a |
| Heptagon (Regular) |  |
7 | 7 | 900° | 7 × 128.57° | 7 | Order 7 | (7/4) × a² × cot(π/7) | 7a |
| Octagon (Regular) |  |
8 | 8 | 1080° | 8 × 135° | 8 | Order 8 | 2(1 + √2) × a² | 8a |
| Trapezium (General) |  |
4 | 4 | 360° | Varies | Depends on symmetry | Order 1 | ½ × (a + b) × h | a + b + c + d |
| Scalene Trapezium |  |
4 | 4 | 360° | All angles different | 0 | Order 1 | ½ × (a + b) × h | a + b + c + d |
| Isosceles Trapezium |  |
4 | 4 | 360° | Varies | 1 | Order 1 | ½ × (a + b) × h | a + 2c + b |
| Rhombus |  |
4 | 4 | 360° | 4 × 90° | 2 | Order 2 | ½ × d1 × d2 | 4a |
| Parallelogram |  |
4 | 4 | 360° | Varies | 0 or 2 | Order 2 | b × h | 2(a + b) |
| Kite |  |
4 | 4 | 360° | Varies | 1 or 2 | Order 1 | ½ × d1 × d2 | 2a + 2b |
🧊 3D Shapes
| Shape | Image | Vertices | Faces | Angles | Lines of Symmetry | Rotational Symmetry | Surface Area | Volume |
|---|---|---|---|---|---|---|---|---|
| Cube |  |
8 | 6 | Each face 90° | 9 | Order 4 (each axis) | 6a² | a³ |
| Cuboid |  |
8 | 6 | Each face 90° | Varies | Order 2 or more | 2(lw + lh + wh) | l × w × h |
| Sphere |  |
0 | 1 curved | 0 | Infinite | Infinite | 4πr² | (4/3)πr³ |
| Cylinder |  |
0 | 3 | 0 | Infinite (around axis) | Infinite | 2πr(h + r) | πr²h |
| Square-based Pyramid |  |
5 | 5 | Varied | 1 | Order 4 | a² + 2a√(h² + (a²/4)) | (1/3)a²h |
| Cone |  |
1 | 2 | 0 | Infinite (around axis) | Infinite | πr(r + l) | (1/3)πr²h |
| Triangular Prism |  |
6 | 5 | Varies | Depends on triangle | Order 1 or more | 2 × Base Area + Perimeter × Height | Base Area × Height |
| Tetrahedron |  |
4 | 4 | Varies | Varies | Order 3 | √3 × a² | (1/6) × √2 × a³ |