2D shapes
2D shapes and tessellation
In this section you name 2D shapes by their properties, put shapes together to make new shapes, and explore which shapes tessellate.
Naming 2D shapes
A polygon is a closed 2D shape made of straight sides. You can name a polygon by counting its sides and vertices: ā¢ triangle ā 3 sides ā¢ square and rectangle ā 4 sides ā¢ pentagon ā 5 sides ā¢ hexagon ā 6 sides ā¢ heptagon ā 7 sides ā¢ octagon ā 8 sides. A circle is not a polygon because it has a curved side.
Properties of shapes
Shapes are described by their properties: ā¢ A square and a rectangle have right angles. ā¢ A rectangle has pairs of parallel sides ā sides that stay the same distance apart and never meet. ā¢ A regular polygon has all sides the same length and all angles equal. ā¢ A semicircle has a curved side.
Putting shapes together
You can put two or more 2D shapes together to make a new shape. Four triangles can be put together to make a square, and three triangles can make a pentagon. You can also draw lines on a shape to divide it into smaller shapes.
Tessellation
Shapes tessellate when they fit together with no gaps and no overlaps, like tiles on a floor. Squares, rectangles, all triangles and regular hexagons tessellate. A regular pentagon does not tessellate on its own, because it leaves gaps.
Worked examples
Naming a shape by its sides
- Count the straight sides of the shape.
- There are 5 sides and 5 vertices.
- A shape with 5 sides is a pentagon.
Answer: The shape is a pentagon.
Describing a property
- You need a shape with at least one right angle.
- A square has a right angle at every corner.
- So a square fits the property.
Answer: A square has at least one right angle.
Making a shape with triangles
- Take three triangles.
- Draw lines on the shape to see if it divides into three triangles.
- The lines fit, so it can be made from three triangles.
Answer: Yes ā the shape can be made with three triangles.
Testing tessellation
- Draw around a square many times, fitting the shapes together.
- Check for any gaps or overlaps.
- There are none, so squares tessellate.
Answer: A square tessellates; a regular pentagon does not.
Where you see this in real life
- Floor and wall tiles that fit together with no gaps.
- A honeycomb made of tessellating regular hexagons.
- Fabric and wallpaper patterns that repeat with no gaps.
Key words
- 2D shape
- A flat shape, such as a triangle, square or circle.
- Polygon
- A closed 2D shape made only of straight sides.
- Vertex
- A corner of a shape where two sides meet (more than one are vertices).
- Parallel
- Sides that stay the same distance apart and never meet.
- Regular
- A polygon with all sides the same length and all angles equal.
- Tessellation
- Shapes fitting together with no gaps and no overlaps.