Measurement | Year 3 Mathematics IGCSE (Cambridge) - Class 3 PDF Download

Introduction

In this chapter, we will learn how to measure lengths, calculate the area, and find the perimeter of different shapes. These are essential skills used in everyday life for tasks like measuring objects, determining the size of spaces, and working with various geometric shapes. By the end of the chapter, you'll be able to apply these concepts to solve real-world problems involving measurement, area, and perimeter!

1. Understanding Measurement

What is Measurement?

Measurement is the process of determining the size, length, or amount of something. It helps us understand how big or small things are, and we use different units to measure various quantities, such as length, weight, and capacity.

Units of Measurement:

There are many units we use to measure things, including:

• Length: centimeters (cm), meters (m), kilometers (km)
• Weight: grams (g), kilograms (kg)
• Capacity: milliliters (ml), liters (l)
• It’s important to know which units to use for different types of measurement. For example, we use meters to measure longer lengths and centimeters for shorter ones.

Measuring Length:

We can measure length using a ruler or measuring tape. To measure a straight line, place the start of the object at the zero point on the ruler, then read the length at the end.

2. Perimeter

What is Perimeter?

Perimeter is the distance around the edge of a shape. It’s like walking around the boundary of a figure.

How to Find Perimeter:

To find the perimeter of a shape, we add the lengths of all its sides. Here are the formulas for common shapes:

• Rectangle: Perimeter = 2 × (Length + Width)
• Square: Perimeter = 4 × Side length
• Triangle: Perimeter = Sum of all three sides
• Example: If the length of a rectangle is 5 cm and the width is 3 cm, the perimeter is:
  Perimeter = 2 × (5 + 3) = 2 × 8 = 16 cm

Perimeter of Irregular Shapes:

For irregular shapes, we simply add the lengths of each side. If a shape has sides of different lengths, measure each one and add them together to find the perimeter.

3. Area

What is Area?

Area is the amount of space inside a shape. It tells us how much surface a shape covers. Area is usually measured in square units, like square centimeters (cm²) or square meters (m²).

How to Find Area:

We use different formulas to find the area of different shapes. Here are some common ones:

• Rectangle: Area = Length × Width
• Square: Area = Side × Side
• Triangle: Area = (Base × Height) ÷ 2
• Example: If the length of a rectangle is 5 cm and the width is 3 cm, the area is:
  Area = 5 × 3 = 15 cm²
  

Area of Irregular Shapes:To find the area of irregular shapes, we can divide the shape into smaller parts (like rectangles or triangles), find the area of each part, and then add them together.

4. Comparing Perimeter and Area

Perimeter vs. Area:

Perimeter tells us the total distance around a shape, while area tells us the total space inside the shape. The perimeter is measured in linear units, while the area is measured in square units.

Example:

Let’s compare the perimeter and area of a rectangle with a length of 6 cm and a width of 4 cm.

• Perimeter: Perimeter = 2 × (6 + 4) = 2 × 10 = 20 cm
• Area: Area = 6 × 4 = 24 cm²
• As you can see, the perimeter is a distance (20 cm), while the area is the amount of space inside the shape (24 cm²).

5. Real-Life Examples of Perimeter and Area

Using Perimeter in Real Life:

1. Building a Fence Around a Playground: If a school wants to build a fence around its playground, the perimeter of the playground will tell the school how much fencing material to buy. If the playground is rectangular, you would add the lengths of all four sides to calculate the perimeter.

2. Installing Baseboards: When installing baseboards along the walls of a room, the perimeter of the room will help you determine how much baseboard trim is needed. You simply measure the lengths of all four walls and add them up to get the total perimeter.

3. Creating a Border for a Flower Bed: If you want to create a flower bed in your garden and add a decorative border, you would calculate the perimeter of the garden bed to know how much stone or wood border you need to purchase.

4. Planning a Running Track: For an outdoor running track, the perimeter is important to know how many laps are needed to cover a specific distance. If the track is oval, you would need to calculate the perimeter to determine how much land the track will cover.

Using Area in Real Life:

1. Laying Down Tiles: If you are remodelling a kitchen and want to lay down tiles on the floor, you need to calculate the area of the floor. This will help you figure out how many tiles to buy, as the area of the floor equals the number of tiles needed to cover it.

2. Gardening: If you want to plant grass, flowers, or vegetables in your backyard, you need to calculate the area of the garden plot to determine how much soil, seeds, or fertiliser you need.

3. Painting a Wall: When painting a room, the area of the walls needs to be calculated to determine how much paint you need. Multiply the height and width of each wall to find the area and know how much paint to buy.

4. Buying Wallpaper: When decorating a room with wallpaper, you need to calculate the area of the walls you are covering. By measuring the height and width of each wall and multiplying them, you can determine how many rolls of wallpaper are necessary.

5. Planning a Pool: If you're designing a swimming pool in your backyard, calculating the area of the pool (especially for rectangular or circular shapes) helps you estimate the amount of water needed and the space it will occupy.

6. Practice Questions:

• Find the perimeter of a square with a side length of 8 cm.
• Calculate the area of a rectangle with a length of 7 cm and a width of 3 cm.
• The sides of a triangle are 6 cm, 8 cm, and 10 cm. Find the perimeter.
• Find the area of a triangle with a base of 4 cm and a height of 5 cm.
• Compare the perimeter and area of a rectangle with a length of 10 cm and a width of 2 cm.
• How much carpet would you need for a room that is 5 meters long and 4 meters wide?