How does a polygon have

Calculate the sum of interior angles in an octagon. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is:.

Calculate the size of the interior angle of a regular hexagon. If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The formula for calculating the size of an exterior angle is:. Calculate the size of the exterior and interior angle in a regular pentagon. For example:. There are names for many different types of polygons, and usually the number of sides is more important than the name of the shape.

A regular polygon has equal length sides with equal angles between each side. Any other polygon is an irregular polygon , which by definition has unequal length sides and unequal angles between sides. Circles and shapes that include curves are not polygons - a polygon, by definition, is made up of straight lines. See our pages on circles and curved shapes for more. The angles between the sides of shapes are important when defining and working with polygons.

See our page on Angles for more about how to measure angles. There is a useful formula for finding out the total or sum of internal angles for any polygon, that is:.

Furthermore, if the shape is a regular polygon all angles and length of sides are equal then you can simply divide the sum of the internal angles by the number of sides to find each internal angle. As well as the number of sides and the angles between sides, the length of each side of shapes is also important.

If your shape is a regular polygon such as a square in the example above then it is only necessary to measure one side as, by definition, the other sides of a regular polygon are the same length.

It is common to use tick marks to show that all sides are an equal length. In the example of the rectangle we needed to measure two sides - the two unmeasured sides are equal to the two measured sides. It is common for some dimensions not to be shown for more complex shapes.

In such cases missing dimensions can be calculated. The missing horizontal length can be calculated. Take the shorter horizontal known length from the longer horizontal known length. The simplest and most basic polygon for the purposes of calculating area is the quadrilateral. To obtain the area, you simply multiple length by vertical height.

For parallelograms, note that vertical height is NOT the length of the sloping side, but the vertical distance between the two horizontal lines. This is because a parallelogram is essentially a rectangle with a triangle cut off one end and pasted onto the other:. You can see that if you remove the left-hand blue triangle, and stick it onto the other end, the rectangle becomes a parallelogram.

Knowledge of shape properties will include angles and symmetry of these polygons. Children will describe shapes and identify them using their properties including symmetry and angles. They might be asked to sort shapes according to their properties using Venn diagrams and Carroll diagrams.

Year 4 Children are taught to compare lengths and angles of polygons to decide if they are regular or irregular. Children will be given a range of polygons to sort into regular and irregular; this might be be completing practical tasks or using ICT. Year 5 Children will be taught to distinguish between regular and irregular polygons based on reasoning about equal sides and angles. Children will be given shapes to sort and asked to explain why the polygon is regular using the properties of angles and sides.

Year 6 At the end of KS2 children begin to find unknown angles in regular polygons. Children will be shown how to calculate unknown angles in polygons using their knowledge of angles and a given formula.

Calculating the size of the angles in a polygon in Year 6 It is important to remember that all the internal angles of a regular polygon are equal. In Year 6 children use this knowledge and the following formula to calculate the size of the angles. More like this. Drawing 2D shapes. What are the names of 2D and 3D shapes? Count the sides of 2D shapes. Mystery 3D shape net.