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Area and Square Units

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 in2 

∴Area of the rectangle A = area of the rectangle B = 30 in2

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 in2 

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. 

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