2D and 3D Shapes
A primary math lesson on 2D and 3D shapes: learn flat shapes, solid shapes, sides, faces, edges and vertices with real-life examples, a table and a quiz.
Key takeaways
- 2D shapes are flat and have length and width, like a circle or square.
- 3D shapes are solid and take up space, like a ball or box.
- 2D shapes have sides and corners; 3D shapes have faces, edges and vertices.
- A face is a flat surface, an edge is where two faces meet, and a vertex is a corner.
- Many 3D shapes are built from 2D shapes, like a cube made of squares.
Flat Shapes and Solid Shapes
Shapes are all around us. Some shapes are flat, like the shapes you draw on paper. Other shapes are solid, like the things you can pick up and hold. In math, we sort shapes into two big groups: 2D shapes and 3D shapes.
- 2D means "two-dimensional." These shapes are flat. They have length and width but no thickness. You can draw them but you cannot pick them up off the page.
- 3D means "three-dimensional." These shapes are solid. They have length, width, and depth, so they take up space. You can hold them in your hand.
Think of it this way: a drawing of a circle is 2D, but a real ball is 3D. The drawing is flat; the ball is solid.
Common 2D Shapes
Let's meet some flat shapes. We describe 2D shapes by their sides (the straight edges) and their corners (where two sides meet).
| 2D shape | Sides | Corners | Looks like |
|---|---|---|---|
| Circle | 0 (curved) | 0 | A clock, a coin |
| Triangle | 3 | 3 | A slice of pizza, a roof |
| Square | 4 (equal) | 4 | A cracker, a tile |
| Rectangle | 4 | 4 | A door, a book |
| Pentagon | 5 | 5 | A house outline |
A circle is special because it has no straight sides at all. Its edge is one smooth curve.
A square and a rectangle both have 4 sides and 4 corners, but on a square all four sides are the same length. On a rectangle, two sides are long and two are short. You can explore more flat shapes in shapes all around us.
Common 3D Shapes
Now let's meet the solid shapes. For 3D shapes we use three special words:
- Face — a flat surface on the shape (like one side of a box).
- Edge — the line where two faces meet.
- Vertex — a corner where edges meet. (More than one vertex are called vertices.)
Here are the most common 3D shapes:
| 3D shape | Faces | Edges | Vertices | Looks like |
|---|---|---|---|---|
| Cube | 6 | 12 | 8 | A dice, a sugar cube |
| Cuboid | 6 | 12 | 8 | A cereal box, a brick |
| Sphere | 0 (curved) | 0 | 0 | A ball, an orange |
| Cylinder | 2 flat + 1 curved | 2 | 0 | A tin can, a battery |
| Cone | 1 flat + 1 curved | 1 | 1 | An ice cream cone, a party hat |
| Square pyramid | 5 | 8 | 5 | The Egyptian pyramids |
A cube is like a dice. It has 6 square faces that are all the same size, 12 edges, and 8 vertices. A cuboid looks like a stretched cube, like a cereal box: still 6 faces, but they are not all squares.
A sphere is a perfect ball. It has no edges and no vertices because it is curved all over. That is exactly why a ball rolls so easily in any direction!
Why Shapes Roll, Slide, or Stack
The faces, edges, and vertices of a shape decide how it moves:
- Flat faces let a shape slide and stack, like boxes piled in a cupboard.
- Curved surfaces let a shape roll, like a ball or a can lying on its side.
- A cylinder can both roll (on its curved side) and stack (on its flat circle faces). It does both jobs!
Try this in your head: a cube cannot roll because every face is flat. A sphere cannot stack because it has no flat face to balance on. Understanding faces explains everything!
2D Shapes Build 3D Shapes
Here is a cool secret: many 3D shapes are made from 2D shapes joined together.
- A cube is made of 6 squares.
- A cuboid is made of 6 rectangles.
- A cylinder has 2 circles (top and bottom) and a curved part.
- A cone has 1 circle and a curved part.
- A square pyramid has 1 square and 4 triangles.
If you cut open a cardboard box and flatten it, you can see the 2D faces. This flat pattern is called a net. Learning 2D shapes first really does help you understand the 3D world!
Spot the Shapes Around You
Math is everywhere. Look around the room:
- A window might be a rectangle (2D) in a wall.
- A tin of beans is a cylinder (3D).
- A football is a sphere (3D).
- A slice of toast can be a square (2D) when you look at the top.
- A party hat is a cone (3D).
The more you look, the more shapes you will find!
Try It Yourself
Have a go at these activities:
- Shape hunt. Walk around your home. Find one cube, one sphere, one cylinder, and one cone. Name each thing you find.
- Count the parts. Pick up a box. Count its faces (6), its edges (12), and its vertices (8). Does it match the cube row in the table?
- Roll or stack? Gather a ball, a tin can, and a box. Test each one. Which roll? Which stack? Which can do both?
- Draw the 2D faces. Look at a cereal box. Draw the flat shapes you would need to make it (6 rectangles).
Now you know flat shapes and solid shapes, and the special words faces, edges, and vertices. You are becoming a shape expert! 🔺🔵🟦
Quick quiz
Test yourself and earn XP
Which of these is a 2D shape?
A triangle is flat, so it is a 2D shape. A cube and sphere are solid 3D shapes.
How many sides does a square have?
A square has 4 equal sides and 4 corners.
What is a face on a 3D shape?
A face is a flat surface on a solid shape, like one side of a box.
How many faces does a cube have?
A cube has 6 square faces, like a dice.
Which 3D shape rolls because it has no flat faces or edges?
A sphere (like a ball) is round all over with no edges or vertices, so it rolls in every direction.
FAQ
2D shapes are flat and only have length and width, like a drawing of a square. 3D shapes are solid and also have depth, so they take up space, like a real box you can hold.
On a 3D shape, a face is a flat surface, an edge is the line where two faces meet, and a vertex is a corner where edges meet. The plural of vertex is vertices.
Many 3D shapes are made from 2D shapes. A cube is made of 6 squares, and a cylinder has 2 circle faces. Learning 2D shapes first helps you understand 3D shapes.
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