Polygon
A polygon is a flat two-dimensional shape with even sides that are fully closed. The sides must be straight, not curved. Polygons can have any number of sides.
Regular and irregular polygons
Polygons can be either regular or irregular. A regular polygon is one in which each side is the same length and at the same angle.
An irregular polygon has sides or angles of differing lengths and sizes. Although it must still have straight sides that are all joined up, or it would not be a polygon.
What is a polygon shape?
A polygon shape is a two-dimensional shape with straight sides that all join up. Here are some examples of polygon shapes:
Regular Triangle
• three equal sides
• three equal angles
Regular Quadrilateral (Square)
• four equal sides
• four equal angles
Regular Pentagon
• five equal sides
• five equal angles
Regular Hexagon
• six equal sides
• six equal angles
Regular Heptagon
• seven equal sides
• seven equal angles
Regular Octagon
• eight equal sides
• eight equal angles
What are some particular kinds of polygons?
Quadrilaterals are polygons with four sides, but quadrilaterals with the same sized sides and angles have a unique name – they are called squares. For example, a rectangle is a rectangle if a polygon has four right-angled corners, but two opposite sides are longer than the other pair of sides.
There are also three different kinds of triangles with unusual names:
- An equilateral triangle, which is regular as all of its sides and angles are the same size
- An isosceles triangle is an irregular-shaped triangle
- A right-angle triangle, named so because one of its angles is a right angle
Concave, convex, simple, and complex polygons
There are several other types of polygons and regular and irregular polygons. For example, a polygon can be regular, irregular, concave, or convex.
When answering the question “what is a polygon?” in KS2, students will be expected to be able to define a convex polygon and a concave polygon.
Here are simple definitions of convex polygons and concave polygons:
- A convex polygon is a shape with no angles pointing in, which means that none of its internal angles measures more than 180°.
- A concave polygon is a shape with some internal angles that are greater than 180°, and these angles will point inwards.
Calculating the size of the angles in a polygon in KS2:
When learning about polygons in KS2, children will learn to use the rule that all internal angles in a regular polygon are equal to help them calculate the size of interior angles in different common shapes. Luckily, they don’t have to measure each angle in a polygon. Instead, a helpful formula can help them work out the interior angles.
Use the following formula to work out the interior angles of a regular polygon:
(n-2)×180º ÷ n
n = the number of sides
So, for example, to work out the interior angles in a regular hexagon:
First, count the number of sides (6)
Secondly, subtract 2 from the number of sides as per the formula (6-2 = 4)
Next, multiply by 180º to learn the sum of all angles in shape (4 ×180º = 720º)
Finally, divide your answer by the number of sides to work out the size of each interior angle in a regular polygon(720º ÷ 6 = 120º).
Examples of polygon shapes
Polygon shapes are all around us. So many objects around us form a polygon, from triangles to decagons, from the natural world to artificial things. We’ve put together a list of the most common polygon shapes, from three-sided shapes to ten-sided shapes, and examples. We’ve also developed some simple rules to help you remember their names!
How to remember the names of polygon shapes
Triangle. Triangles have three sides, so to help us remember, we can think of a tricycle with three wheels. The “tri” at the beginning of the tricycle is the same as “tri” at the beginning of the triangle. Some examples of triangles in real life include a slice of pizza, traffic signs, and a billiards rack!
Quadrilateral. Quadrilaterals have four sides, so that we can think of quad bikes with four wheels. Some examples of quadrilaterals in the real world include a deck of cards, a chess board, and books.
Pentagon. Pentagons have five sides, and we hold a pen with five fingers. Examples of pentagons include the black sections on a football, a pencil, and okra.
Hexagon. Hexagons have six sides, so we can focus on the “x” in the word “hexagon” and the “x” at the end of the word “six”. Some real-life examples of hexagons include honeycombs and metal nuts.
Septagon. Septagons have seven sides, and “sept” sounds similar to “sev” so we can think of a septagon as a “seven-agon”.
Octagon. An octagon has eight sides, so that we can imagine an octopus with eight tentacles. An example of an octagon in the real world is an open umbrella.
Nonagon. Nonagons have nine sides, and nonagons sound very similar to “nine-again”! The US Steel Building in Pittsburgh, Pennsylvania, is a real-world example of a nonagon.
Decagon. Decagons have ten sides, and there are ten years in a decade. Some countries, such as Australia, Belize, and Hong Kong, have ten-sided coins.
