Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Mensuration → Perimeter ↓


Perimeter of Simple Shapes


The perimeter of a shape is the distance around its edges. Imagine you are walking in a park that is shaped like a square. The perimeter would be the total distance you walk to get around the park.

Understanding the perimeter

Perimeter is a useful measurement that helps us understand the size of the boundary of simple shapes. Whether it is fencing around a garden or drawing a picture, knowing the perimeter gives us the necessary information.

Perimeter of a square

A square is a simple shape with four equal sides. To find the perimeter of a square, you add the lengths of the four sides. Since all sides are equal, you can simply multiply the length of one side by 4.

Formula for the perimeter of a square:

Perimeter = 4 × side length

Example: If the side of a square is 5 units:

Perimeter = 4 × 5 = 20 units
5 units

Perimeter of a rectangle

The opposite sides of a rectangle are equal. The perimeter of a rectangle is the sum of all its sides, which can be calculated using the lengths of the opposite sides.

Formula for the perimeter of a rectangle:

Perimeter = 2 × (length + breadth)

Example: If the length is 8 units and the width is 3 units:

Perimeter = 2 × (8 + 3) = 2 × 11 = 22 units
8 units 3 units

Perimeter of a triangle

A triangle has three sides. To find its perimeter, add up the lengths of the three sides.

Formula for the perimeter of a triangle:

Perimeter = side1 + side2 + side3

Example: If the sides of a triangle are 5 units, 6 units, and 7 units:

Perimeter = 5 + 6 + 7 = 18 units
5 units 6 units 7 units

Circumference (Circumference) of a circle

Although a circle doesn't have sides like polygons, it does have a boundary that we measure. The perimeter of a circle is known as the circumference. To calculate the circumference, you need the radius or diameter of the circle.

Formula of Perimeter:

Circumference = 2 × π × radius

Or

Circumference = π × diameter

Here, π (pi) is approximately 3.14159.

Example using radius: If the radius is 4 units:

Perimeter = 2 × π × 4 = 8π ≈ 25.13 units

Example using diameter: If the diameter is 10 units:

Perimeter = π × 10 = 10π ≈ 31.42 units
Diameter = 100 units radius

Practical applications of perimeter

Knowing how to calculate the perimeter of different shapes can have many practical applications. Here are some examples:

  • If you need to put a fence around a rectangular piece of land, knowing the perimeter can help you buy the right amount of fencing materials.
  • When building a track for walking or running, the perimeter can help determine how long the path needs to be to reach the desired distance.
  • Framing a picture or painting requires knowledge of the perimeter to ensure the frame fits properly.

Challenges and exercises

Here are some exercises to practice the concept of perimeter. Try solving them yourself!

Exercise 1:

You have a rectangular shaped garden. Its length is 12 units and width is 7 units. What is the perimeter of the garden?

Exercise 2:

A square board game needs a border. If one side of the board is 15 units, how much material will be needed to make the border?

Exercise 3:

The lengths of the sides of a triangular park are 9 units, 12 units and 15 units. Calculate the total length of the fence required to enclose the park.

Conclusion

Understanding the perimeter of simple shapes is a basic skill in geometry and math. By practicing and experimenting with these concepts, students can gain confidence in their ability to measure and work with different shapes. The formulas are straightforward, but they are incredibly useful in solving real-world problems.


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Perimeter of Simple Shapes

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