### Key Concepts

- Area
- Square Units

## **Area**

The area is the space taken up by a flat shape.

### How to find the area of a shape?

To find the area of a rectangular shape, multiply its width by its height.

How many squares does this green rectangle cover?

It covers 6 squares.

Its area is 6 square units**.**

We use a unit of area** **to know precisely how a shape is measured.

For example, if each square in the grid above is 1 square meter, then the area of the green rectangle is 6 square meters**.**

We can write 6 square meters as** 6 m²**. This is read as ‘6 square meters’.

### How to Find the Area of Rectangles and Squares

**Rectangles **and **squares **are two of the most common shapes.

Here are a few examples of rectangular objects:

Examples of square objects:

### Area of a Rectangle

To know the area of the rectangle, we count the number of squares** **it covers.

Another way is to multiply the length of the sides**.**

In a rectangle, opposite sides are equal**.**

The length of the sides that go from left to right is called width**.**

The length of the sides that go from top to bottom is called height or length**.**

To find the area of a rectangle**, **multiply the width by the height

**Area = Width ****×**** Height**

Let’s use this formula to find the width of the green rectangle.

First, know the width and height.

The width is 3 square units, and the height is 2 square units.

Now, multiply the width by height.

3 × 2 = 6 square units

If 1 square unit is 1 square meter, then 6 square units is 6 square meters (6 m²).

### Area of a Square

A square has 4 equal sides.

This means that the length of the sides is the same

To find the area of a square**, **multiply the length of 1 side by itself.

**What is the area of this square?**

The length of each side is 3.

3 × 3 = 9 square units

The area of the square is 9 square units

If 1 square unit is 1 centimetre, then 9 square units are 9 square centimetres (9 cm²).

**No Grids:**

If there are no grids with squares to help you, you can still figure out the area of a shape.

To find the area of a rectangle**, **multiply**:**

To find the** **area of a square**, **multiply**:**

**Perimeter**

Perimeter is the length or distance around a shape

How to find a perimeter?

To find the perimeter of a shape. Add the lengths of all the sides.

**Example 1:**

**The shapes below have the same perimeter but different area**

What is the area of rectangle B?

From the above shapes, we have the height and width of rectangle A. We can use these to find its perimeter.

We do that by adding the length of all its sides.

4 + 4 + 3 + 3 = 14 meters

i.e., the perimeter of rectangle B is also 14 meters.

We can’t figure out the area of B yet because the length of one side is still missing.

How do we find the missing side?

We know that the width is 2 meters.

Since **opposite sides are equal**, we double that to get the sum of two sides.

2 + 2 = 4

Now, we **subtract** the sum we got from the total perimeter.

14 – 4 = 10

This means that the sum of the two unknown sides is 10 m.

We divide it by 2, to get the length of each unknown side.

10 ÷ 2 = 5

Now we know that the height of rectangle B is** **5 meters

Let’s see if this is correct by comparing its perimeter with rectangle A’s perimeter.

5 + 2 + 5 + 2 = 14 meters

Now, we got the missing side of rectangle B.

Let’s find the area.

To find the area, we multiply the length and breadth of rectangle B.

∴Area of the rectangle B = 2 × 5 = 10 square meters.

**Example 2:**

**The rectangles below have the same area, but different perimeter**

**What is the perimeter of rectangle A?**

To find the perimeter of a rectangle, we need to know its height and width.

From the above shapes, we have the width of rectangle A. Height is missing.

**How to find the height of rectangle A?**

We know that area of the two rectangles is equal.

First, we need to find the area of rectangle B.

Area of rectangle B = height × width

= 5 × 6 = 30 in^{2}

∴Area of the rectangle A = area of the rectangle B = 30 in^{2}.

Now, we have to find the perimeter of rectangle A

We know that the width of rectangle A is 3 inches, and its area is 30 in^{2}

A = H × W

30 = H × 3

H = 30 ÷ 3 = 10 inches

The missing side is 10 inches

∴The perimeter of the rectangle A = 3 + 3 + 10 + 10 = 26 inches.

What Have we Learnt:

- Understand the meaning of an area
- Use square units to find the area of plane figures made of squares and half squares
- Compare areas of plane figures and make plane figures of the same area
- Solve different questions using plane figures

## Exercise:

1. Jhakia and Modrez have a garden. Jhakia built a fence around her garden that was 6 feet wide and 10 feet long. Modrez built a fence for his garden that was 12 feet wide and 2 feet long. Who’s garden has the greatest area?

2. Molly and Ted built pens for their dogs. Molly made a pen 12 meters by 8 meters. Ted’s pen is 15 meters by 6 meters. Who’s pen has the greatest area?

3. The longer side of a rectangle is 5 m and the shorter side is 2 m. What is the area of the rectangle?

4. A swimming pool is 8 meters wide and 9 meters long. What is the area of the pool in square meters?

5. The surface of a workbook is 10 inches long and 8 inches wide. What is its area?

6. Mrs Pickett’s vegetable garden is 6 feet long and 4 feet wide. She divided her garden into 1 foot squares, and began planting vegetable seeds. So far she has planted seeds in 7 squares. How many squares are left for her to plant?

7. A rectangular classroom has an area of 300 square feet. The rectangular closet next to the classroom has an area of 20 square feet. Which expression shows how to find the total area of the classroom and closet?

8. Each side of a square piece of gold is 10 millimetres long. What is the piece of gold’s area?

9. What is the area of the rectangle if the length is 9 inches and the width is 4 inches?

10. Mr Popper needs to build an icebox for his penguin. The length is 7 ft and the width is 5 ft. What is the area of the icebox?

### What we have learnt:

- Understand the meaning of an area
- Use square units to find the area of plane figures made of squares and half squares
- Compare areas of plane figures and make plane figures of the same area
- Solve different questions using plane figures

**Concept Map:**

**Area & Perimeter**

**Perimeter (p): The distance around the outside of a shape**

**Area (A): The Number of square units inside a shape.**

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: