# 2D Shapes and Quadrilaterals Worksheets, Questions and Revision

## Specification Points Covered

## 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

## 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.

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

## 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**.

## 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:

**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.

## Triangles:

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

**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.

## Example Questions

**Question 1:** State the name of the shape below.

**[1 mark]**

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

**Question 2:** ABCD is a quadrilateral. AB is parallel to CD. State which type of quadrilateral ABCD is.

**[1 mark]**

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

**Question 3:** ABCD is a parallelogram. Angle ABC is 56\degree. Calculate the size of angle x.

**[2 marks]**

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