Shapes and solids

2D shapes are flat, like squares and circles. 3D shapes (solids) have depth, like cubes and cylinders. We describe them by their sides, corners (vertices), faces and edges.

Key facts

  • Triangle 3 sides, quadrilateral 4, pentagon 5, hexagon 6, octagon 8.
  • Regular shapes have all sides and angles equal.
  • Faces are flat surfaces, edges are where faces meet, vertices are corners.
  • Euler: faces + vertices − edges = 2 for these solids.

Worked examples

Example 1

How many sides does a hexagon have?

  1. Count the straight sides: 6.
  2. Hex means 6, like a honeycomb cell.

Answer: 6

Example 2

How many faces, edges and vertices does a cube have?

  1. Faces: top, bottom and 4 sides = 6.
  2. Edges: 4 on top, 4 on the bottom, 4 upright = 12.
  3. Vertices: 4 on top, 4 on the bottom = 8.
  4. Check Euler: 6 + 8 − 12 = 2

Answer: 6 faces, 12 edges, 8 vertices