Grade 4
  1. Numbers and Place Value  1.1. Understanding Place Value  1.2. Reading and Writing Large Numbers  1.3. Comparing and Ordering Numbers  1.4. Rounding Numbers  1.5. Understanding Odd and Even Numbers  1.6. Number Patterns and Sequences
  2. Addition and Subtraction  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Estimation in Addition and Subtraction  2.4. Word Problems on Addition and Subtraction
  3. Multiplication and Division  3.1. Understanding Multiplication  3.2. Multiplying Multi-Digit Numbers  3.3. Understanding Division  3.4. Dividing Multi-Digit Numbers  3.5. Multiplication and Division Facts  3.6. Word Problems on Multiplication and Division
  4. Factors and Multiples  4.1. Understanding Factors  4.2. Finding Common Factors  4.3. Understanding Multiples  4.4. Finding Common Multiples  4.5. Prime and Composite Numbers  4.6. Prime Factorization  4.7. Greatest Common Factor  4.8. Least Common Multiple
  5. Fractions  5.1. Understanding Fractions  5.2. Equivalent Fractions  5.3. Simplifying Fractions  5.4. Comparing and Ordering Fractions  5.5. Addition of Fractions  5.6. Subtraction of Fractions  5.7. Mixed Numbers and Improper Fractions  5.8. Converting Mixed Numbers to Improper Fractions  5.9. Word Problems on Fractions
  6. Decimals  6.1. Understanding Decimals  6.2. Reading and Writing Decimals  6.3. Comparing and Ordering Decimals  6.4. Rounding Decimals  6.5. Addition of Decimals  6.6. Subtraction of Decimals  6.7. Converting Decimals to Fractions  6.8. Converting Fractions to Decimals  6.9. Word Problems on Decimals
  7. Measurement  7.1. Length  7.1.1. Units of Length  7.1.2. Converting Units of Length  7.1.3. Perimeter  7.1.4. Area  7.1.5. Word Problems on Length  7.2. Weight  7.2.1. Units of Weight  7.2.2. Converting Units of Weight  7.2.3. Word Problems on Weight  7.3. Volume and Capacity  7.3.1. Units of Volume  7.3.2. Converting Units of Volume  7.3.3. Estimating Volume and Capacity  7.3.4. Word Problems on Volume and Capacity  7.4. Time  7.4.1. Reading Time  7.4.2. Units of Time  7.4.3. Converting Units of Time  7.4.4. Calculating Elapsed Time  7.4.5. Word Problems on Time
  8. Geometry  8.1. Properties of Shapes  8.1.1. Types of Angles  8.1.2. Types of Triangles  8.1.4. Symmetry  8.1.5. Lines of Symmetry  8.2. Perimeter and Area  8.2.1. Perimeter of Rectangles  8.2.2. Perimeter of Other Shapes  8.2.3. Area of Rectangles  8.2.4. Area of Other Shapes  8.2.5. Area of Irregular Shapes  8.3. Coordinate Geometry  8.3.1. Understanding Coordinates  8.3.2. Plotting Points on a Grid  8.3.3. Identifying Shapes on a Grid
  9. Data and Graphs  9.1. Types of Data  9.2. Organizing Data  9.3. Reading Bar Graphs  9.4. Drawing Bar Graphs  9.5. Line Plots  9.7. Reading and Interpreting Line Graphs  9.8. Word Problems on Graphs
  10. Money  10.1. Understanding Money  10.2. Addition and Subtraction with Money  10.3. Making Change  10.4. Multiplying and Dividing Money  10.5. Word Problems on Money

Grade 4 → Geometry ↓


Perimeter and Area


Introduction

In this explanation, we will talk about two important concepts in geometry: perimeter and area. These are mathematical terms that help us understand the shape of various shapes. While area deals with the space inside a shape, perimeter is about the distance around the shape. Let's learn more about both these concepts with examples and simple explanations.

What is the perimeter?

The perimeter of a shape is the total length of its boundary. Imagine you walk around the boundary of a park; the distance you cover is the perimeter of the park. Calculating the perimeter involves adding up the lengths of each side of the shape. Let's look at some examples to understand this concept better.

Example 1: Perimeter of a rectangle

A rectangle has four sides, and the opposite sides are equal in length. Let us take a rectangle of 8 units length and 4 units width. To find the perimeter, we add the lengths of all the sides.

Length = 8 units
Width = 4 units

Perimeter = length + width + length + width
          = 8 + 4 + 8 + 4
          = 24 units
8 units 4 units

Example 2: Perimeter of a triangle

A triangle has three sides. For a triangle with sides of 5 units, 6 units, and 7 units, we add the lengths of all the sides to find the perimeter.

Side 1 = 5 units
Side 2 = 6 units
Side 3 = 7 units

Perimeter = side 1 + side 2 + side 3
          = 5 + 6 + 7
          = 18 units
7 units 6 units 5 units

How to calculate the perimeter: a general formula

To find the perimeter of any polygon, simply add up the lengths of all its sides. For a figure with n sides, where each side has a different length, you can use the formula:

 Perimeter = Side1 + Side2 + ... + Side

What is the area?

The area of a shape is the amount of space inside its boundary. Think of the floor space covered by a carpet. This is the area the carpet covers. Calculating area depends on the type of shape. We will look at a few different shapes to understand how area is calculated.

Example 1: Area of a rectangle

The area of a rectangle can be found by multiplying its length by its width. For example, the area of a rectangle with a length of 8 units and a width of 4 units is:

Length = 8 units
Width = 4 units

Area = length × breadth
     = 8 × 4
     = 32 square units
8 units 4 units

Example 2: Area of a triangle

The formula for finding the area of a triangle is slightly different. The area of a triangle is calculated using its base and height. Here is the formula:

Area = (base × height) / 2

For example, for a triangle with a 10 unit base and 5 unit height:

Base = 10 units
Height = 5 units

Area = (10 × 5) / 2
     = 50 / 2
     = 25 square units
Base = 10 units Height = 5 units

How to calculate area: a general approach

The way to find the area depends on the shape:

  • Rectangle: Area = Length × Width
  • Square: Since all sides are equal: Area = Side × Side
  • Triangle: Area = (Base × Height) / 2

Relation between perimeter and area

While both perimeter and area involve measuring space and size, it's important to understand that they describe different aspects of a shape. Knowing the perimeter is like knowing how much fencing you need to enclose the garden, while knowing the area is like knowing how many tiles you need to cover the garden.

For example, two rectangles can have the same area but different perimeters. Consider two rectangles, one of which has a length of 6 units and a width of 4 units, and the other of which has a length of 3 units and a width of 8 units. Both have an area of 24 square units, but their perimeters are different.

Verse 1:
Length = 6, Width = 4
Area = 6 × 4 = 24
Perimeter = 6 + 4 + 6 + 4 = 20

Verse 2:
Length = 3, Width = 8
Area = 3 × 8 = 24
Perimeter = 3 + 8 + 3 + 8 = 22

Conclusion

Understanding perimeter and area is important to understanding the basic concepts of geometry. These measurements allow us to compare shapes and understand their dimensions. While perimeter helps us understand lengths and boundaries, area gives us information about the space that a shape occupies. By practicing with different shapes and sizes, students can develop a solid understanding of these concepts, helping them in both mathematical and real-world applications.

Understanding these concepts through hands-on activities, such as measuring objects around us or making models out of paper, can be a fun and engaging way to deepen understanding of area and perimeter.


Grade 4 → 8.2


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Perimeter and Area

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