# Geometrical shapes

Small children may be interested in the kinds of shapes they see from day to day. If you talk about geometrical shapes – both flat and solid – it can be a useful exercise in pattern recognition, which is so vital in general mathematical understanding. It also helps their observation and may give a useful foundation for art or technology. Once you start looking, you’ll see shapes all over the place! You could perhaps create a list of objects that have regular shapes, or draw them, or make a collage from digital photos.

The easiest shape to recognise is a circle. It has no straight edges, and drawing one accurately is difficult by hand. You can see circles all over the place: a ring is circular, so is a biscuit, or a counter in many board games. Wheels are circular too.

An elongated circle, as if it’s been stretched, is called an oval: You don’t see so many of these in everyday life, but you might have a bathroom light or mirror that’s oval. Actually this shape is technically called an ellipse; an oval is a more general term for anything egg-shaped, so that one side can be fatter than the other.

Most shapes, however, are drawn with straight lines. A triangle is the simplest shape: . This diagram shows an equilateral triangle – one that has all three sides of exactly the same length. In an orchestra the instrument called a triangle is a simple piece of metal which this shape.

The word ‘equilateral‘ is from Latin, meaning ‘equal sides’. The word ‘triangle’ is from Greek, where ‘tri’ is from the word meaning ‘three’. There are other words using this, such as tripod (something with three legs) or tricycle (something with three wheels).

You can make triangles that are not equilateral, of course. They can be tall, thin ones or short, fat ones, or totally irregular ones. To be a triangle, the shape simply has to have three sides.

If you have a shape with four equal and straight sides, it’s a square: This is another regular shape – or polygon, if you want to use the official term. The word ‘polygon’ is also from Greek: ‘poly‘ means ‘several’ (or ‘a lot’) and ‘gon‘ means ‘sides’.

This is a rectangle or oblong shape. It’s one of the most commonly seen shapes in everyday life. Look at a curtain, or a pillowcase, or a table-top, or even a wall. With some exceptions, they’re mostly rectangles. A rectangle has four sides, and four square corners, but two of the sides are longer than the other two. A square is actually a specific type of rectangle that has all four sides the same.

This related shape is a diamond or rhombus.

If you squash a square, so that you still have four equal sides but they’re no longer straight, this is what you get. It’s also a special instance of a parallelogram, which is like a squashed rectangle.

This five-sided figure is a regular pentagon.

The prefix pente- comes from the Greek, meaning five. You don’t see many of these in everyday life, but a child’s drawing of a house tends to be five-sided, even if the sides aren’t the same lengths.

A six-sided figure is a hexagon.

Not surprisingly, the prefix hex- is from the Greek, meaning six. Hexagons are the shapes found in honeycombs. You can divide a hexagon into six equilateral triangles if you draw three lines from each pair of opposite corners.

There are many more polygons – if you know the Greek numbers, you can usually guess the names of the shapes with that number of sides. A heptagon is a seven-sided figure, an octagon is an eight-sided figure, and so on.

If you’re interested in knowing more about angles and how to measure them, see the page on understanding angles. If you’d like to know about the regular solids – cubes and so on – see the page on geometric solids.

For more articles about teaching basic maths without workbooks or drill, see: