Polygons

• A polygon is a 2D shape with at least three sides and is regular if all the sides are equal and all angles are equal.

• In order to work out the size of missing interior angles angles in polygons, it is important to know what the interior angles of each polygon add up to.

• To find the size of one interior angle of a regular polygon, divide the sum of the interior angles by the number of sides.

Make sure you are confident in finding the value of missing angles before working with polygons.

A triangle is a 2D shape or polygon with three sides.

There are four different types of triangle, with different properties.

• An equilateral triangle has three sides of equal length. All of the angles are 60°.
• An isosceles triangle has two sides of equal length and two equal angles.
• A right-angled triangle is a triangle that has one angle that is a right-angle or 90°.
• A scalene triangle has three sides of different lengths and unequal angles.

Remember

• The angles in a triangle always add up to 180°.

• Recognising the type of triangle can be useful in calculating the sizes of unknown angles.

Find out more about triangles, along with a worked example below

A quadrilateral is a 2D shape or polygon with four sides. There are different types of quadrilaterals, each with different properties.

• These include square, rectangle, rhombus, parallelogram, trapezium, kite and arrowhead.

• Properties of a quadrilateral include the length of their sides, size of their angles, their diagonals and their symmetry.

• A specific property may apply to more than one quadrilateral.

• Angles in a quadrilateral always add up to 360°.

Recognising the type of quadrilaterals can be useful in calculating the sizes of unknown angles.

Find out more about quadrilaterals and their properties below

A polygon is a 2D shape with three or more sides.

The polygon is regular if all its sides and angles are the same size. For polygons:

• an interior angle and an exterior angle add up to 180°
• the interior angles of any polygon add up to (number of sides – 2) × 180°

For a regular polygon the size of one exterior angle = 360 ÷ 𝑛, where 𝑛 is the number of sides.

The table below shows the sum of interior angles for some regular polygons. It also shows the sizes of their interior and exterior angles.

The interior and exterior angles for the heptagon are rounded to the nearest degree.

Find out more below, along with a worked example

Practise what you've learned about polygons with this quiz.

Now you've revised polygons, why not look at nets, plans and elevations?