2D Shapes and Quadrilaterals Worksheets | Questions and Revision

2D Shapes and Quadrilaterals Worksheets, Questions and Revision

Level 1-3

2D Shapes

A polygon is a shape made up of straight edges

There are two types of polygons you need to know about: 

  • Regular – All sides and angles are the same
  • Irregular – All sides and angles are not the same
KS3 Level 4-5

Regular Polygons

You will already be familiar with the names of some shapes, but it’s important to recognise the names of shapes that have up to 10-sides, as seen below.

All the shapes below are regular polygons, meaning all the sides in one shape are the same length. 

2D Shapes needed for GCSE Maths

All of these shapes are regular polygons, meaning that all of their sides are the same length and all the angles are the same.

KS3 Level 1-3

Irregular polygons 

Look at the irregular shapes shown:

Shape A – Counting the number of sides, we see that shape \textcolor{red}{A} has 4 sides, therefore it is a quadrilateral.

Shape B – Doing the same for \textcolor{blue}{B}, we see that it has 7 sides, and therefore it is a heptagon.

irregular Polygons
KS3 Level 1-3

Quadrilaterals : 6 Common Types

Triangles and quadrilaterals are the shapes we will see most often. As a result, we have names for specific types of them.

The different types of quadrilaterals you should be familiar with are:

6 common quadrilaterals

1. Square – Has 4 sides equal in length, and 4 equal angles (all 90\degree).

2. Rectangle – Has 4 equal angles (all 90\degree), and its opposite sides are equal in length.

3. Trapezium – Has one pair of parallel sides.

4. Kite – Has two pairs of equal sides, and each pair must be adjacent to each other. Additionally, two of its angles (as marked on the picture) are equal.

5. Parallelogram – Has two pairs of parallel sides. Additionally, opposite angles are equal and adjacent angles add to 180\degree.

6. Rhombus – Has 4 sides equal in length. Additionally, opposite angles are equal, and opposite sides are parallel.

6 common quadrilaterals
KS3 Level 1-3

Triangles: 

The different types of triangles you should be familiar with are:

Common Triangles GCSE Maths

1. Equilateral – Has 3 sides equal in length, and all 3 angles are 60\degree.

2. Isosceles – Has 2 sides equal in length, and the two base angles are equal.

3. Right-angled – Has 1 angle equal to 90\degree.

4. Scalene – Has 3 sides of different lengths, and no angles are the same.

Common Triangles GCSE Maths
KS3 Level 1-3

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Example Questions

This shape has 5 sides, so it is an irregular pentagon.

The only feature this quadrilateral has is one pair of parallel sides. Therefore, it must be a trapezium.

In a parallelogram, adjacent angles add to 180\degree, and angle x is adjacent to ABC, so we get that

 

x\degree=180\degree-56\degree=124\degree

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