Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Mensuration ↓


Perimeter and Area


Introduction

In mathematics, especially geometry, two fundamental concepts we often encounter are perimeter and area. These concepts help us understand the size and shape of various geometric shapes. Perimeter refers to the distance around a two-dimensional shape, while area is the measure of the space inside it.

As we go deeper, we'll explore how to calculate perimeter and area for different shapes, from simple rectangles and triangles to more complex shapes like circles.

What is the perimeter?

The perimeter is the total length of the boundary or outline of a two-dimensional shape. Imagine a fence around a playground; the length of the fence is the perimeter of the playground.

Calculating the perimeter for regular shapes like rectangles, squares, and triangles is simple. Let's learn how we calculate the perimeter for different shapes.

Perimeter of a rectangle

A rectangle has four sides, with opposite sides being equal. To find the perimeter of a rectangle, we add the lengths of the four sides.

Perimeter of Rectangle = 2 * (Length + Width)

For example, if the length of a rectangle is 10 units and the width is 5 units, then the perimeter will be:

Perimeter = 2 * (10 + 5) = 2 * 15 = 30 units
width = 5 length = 10

Perimeter of a square

All the sides of a square are of equal length. Therefore, calculating the perimeter is even easier.

Perimeter of Square = 4 * Side

For example, if each side of a square measures 8 units, its perimeter is:

Perimeter = 4 * 8 = 32 units
Side = 8

Perimeter of a triangle

To calculate the perimeter of a triangle, you simply need to add the lengths of its three sides. Triangles may differ in their type - equilateral, isosceles or scalene - but the perimeter formula remains the same.

Perimeter of Triangle = Side 1 + Side 2 + Side 3

If the measures of the sides of a triangle are 3 units, 4 units and 5 units, then:

Perimeter = 3 + 4 + 5 = 12 units
Side = 4 Side = 5 Side = 3

What is the area?

Area is the measure of the space inside a two-dimensional shape. While perimeter is about the boundary, area measures the entire surface. Think of it as the space a shape covers or how much paint you would need to coat its insides.

Area of a rectangle

For a rectangle, the area is calculated by multiplying its length by its width.

Area of Rectangle = Length * Width

The area of a rectangle of length 10 units and breadth 5 units is:

Area = 10 * 5 = 50 square units

Area of a square

Since all the sides of a square are equal, its area can be easily found by squaring the length of one of its sides.

Area of Square = Side * Side

If the side of a square is 8 units, then its area will be:

Area = 8 * 8 = 64 square units

Area of a triangle

The area of a triangle is found using the base and the height. The base can be any side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.

Area of Triangle = 1/2 * Base * Height

For a triangle with an 8 unit base and 5 unit height, the area can be calculated as:

Area = 1/2 * 8 * 5 = 20 square units
height = 5 Base = 8

Exploring circles: Perimeter and area

While the perimeter of a circle is not usually referred to as such, it does have a similar characteristic called the circumference. The circumference is the distance around a circle.

Circumference of a circle

To calculate the circumference we use the radius, which is the distance from the center of the circle to its edge.

Circumference = 2 * π * Radius

If the radius of a circle is 7 units, then its circumference will be approximately:

Circumference ≈ 2 * 3.14 * 7 ≈ 44 units

Area of a circle

To find the area of a circle, use the radius given in the formula:

Area = π * Radius 2

The area of a circle of radius 7 units is approximately:

Area ≈ 3.14 * 7 2 ≈ 153.86 square units
Radius = 7 π ≈ 3.14

Applications of perimeter and area

Understanding perimeter and area is important in practical scenarios. For example:

  • When designing a garden, perimeter fencing helps establish the necessary boundary fencing.
  • When laying carpet, knowing the area ensures that you purchase enough material to cover the entire floor.
  • When painting a wall, calculating the area helps in estimating the amount of paint needed.

These concepts are not limited to academic practice, but also apply to everyday tasks involving spatial arrangement and planning.

Conclusion

Perimeter and area are fundamental concepts in geometry that provide important information about the dimensions and space occupied by shapes. Whether rectangular, triangular or circular, understanding how to measure and calculate these properties allows for better practical understanding and application in real life.

This strong foundation paves the way for tackling more advanced mathematical problems as we move forward in the learning journey.


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Perimeter and Area

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