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


Measurement is a branch of mathematics that deals with the measurement of various geometric shapes and sizes. A fundamental concept in measurement is "perimeter". In this detailed guide, we will discuss in detail what perimeter is, how to calculate it, and several examples for a complete understanding.

What is the perimeter?

In simple terms, the perimeter is the total length of the boundary or outline of a two-dimensional figure. Imagine you are walking along the edge of a playground; the distance you cover will be the perimeter of that playground.

Perimeter of basic geometric shapes

1. Perimeter of a square

A square is a shape that has four equal sides. The formula for finding the perimeter of a square is:

Perimeter = 4 × side length

For example, if the side of a square is 5 units, then the perimeter will be:

Perimeter = 4 × 5 = 20 units
5

2. Perimeter of a rectangle

A rectangle has two pairs of equal opposite sides. The formula for the perimeter of a rectangle is:

Perimeter = 2 × (length + width)

The perimeter of a rectangle of length 7 units and width 3 units is:

Perimeter = 2 × (7 + 3) = 20 units
73

3. Perimeter of a triangle

A triangle has three sides. To find the perimeter, you simply add the lengths of all the sides together:

Perimeter = side1 + side2 + side3

Consider a triangle where the sides are 3 units, 4 units and 5 units. The perimeter will be:

Perimeter = 3 + 4 + 5 = 12 units
435

4. Circumference of a circle (Circumference)

The perimeter of a circle is called its circumference. The formula for finding the circumference is:

Circumference = 2 × π × radius

If the radius of a circle is 10 units, then the circumference will be:

Circumference = 2 × π × 10 ≈ 62.8 units
10

Practical examples of perimeter

Example 1: Garden fencing

Imagine you have a rectangular garden 15 meters long and 10 meters wide, and you want to build a fence around it. To find out how much fencing material you need, calculate the perimeter:

Perimeter = 2 × (length + width) = 2 × (15 + 10) = 50 meters

You will need 50 meters of fencing material.

Example 2: Image bordering

You have a photo that is 8 inches long on either side. You want to put a border around it. Determine how much border you need by calculating the perimeter of the photo:

Perimeter = 4 × side = 4 × 8 = 32 inches

You will need a 32 inch border for the picture.

More complex shapes

Understanding perimeter is not limited to just basic shapes. Let's understand more complex shapes.

1. Perimeter of regular polygons

A regular polygon is a shape whose all sides and angles are equal. The perimeter of a regular polygon can be calculated as follows:

Perimeter = number of sides × length of one side

The perimeter of a regular pentagon (5 sides) with each side 6 units long is:

Perimeter = 5 × 6 = 30 units
6

2. Perimeter of irregular shapes

For shapes that aren't regular or have different side lengths, you add the lengths of each side separately to find the perimeter.

Consider a figure whose sides measure 3 units, 5 units, 7 units, and 4 units. The perimeter is calculated as follows:

Perimeter = 3 + 5 + 7 + 4 = 19 units
3574

Uses of perimeter in real life

The concept of perimeter can be applied in a variety of real-world scenarios, such as engineering design, crafting, landscaping, architecture, and more. Solving problems involving perimeter helps develop spatial awareness and problem-solving skills.

Real life example: the path around the pool

Let's say you want to create a path that goes around a circular pool with a radius of 12 meters. To find the length of the path, simply calculate the circumference of the pool:

Circumference = 2 × π × 12 ≈ 75.4 meters

You will need approximately 75.4 metres of material for the path around the pool.

Conclusion

Perimeter is a fundamental concept that involves much more than just measuring boundaries. It involves understanding the properties of shapes, applying logical reasoning, and being innovative in finding the perimeter of new shapes. With practice and practical application, anyone can master calculating perimeter and effectively apply this knowledge in various aspects of life.


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Perimeter

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