Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Mensuration ↓


Area and Perimeter


Introduction

In mathematics, measurement is the branch that deals with the various formulas used for length, area, and volume of various geometric shapes. In this detailed explanation, we will focus on understanding two fundamental concepts: area and perimeter. These concepts are applicable in everyday life, such as in construction, agriculture, and designing, as they help us measure the size of objects.

Understanding the perimeter

The perimeter is the total length of the boundary of a two-dimensional shape. Imagine you are wrapping a thread around the edges of a shape; the length of the thread required to wrap it completely is the perimeter of the shape. Perimeter is measured in units of length such as meters, centimeters or feet.

Perimeter of common shapes

Square

A square is a shape that has four equal sides. To find the perimeter of a square, you can add the lengths of the four sides. Since all sides are equal, it can also be found by multiplying the length of one side by 4.

Perimeter of a Square = 4 × side

Example:

If one side of a square is 5 m, then its perimeter is:

Perimeter = 4 × 5 = 20 meters

Let's imagine a square:

5 m

Rectangle

A rectangle is a shape whose opposite sides are equal. To find its perimeter, you add the lengths of all the sides. Since opposite sides are equal, the formula can be simplified by adding the length and width and then multiplying by 2.

Perimeter of a Rectangle = 2 × (length + width)

Example:

If the length of a rectangle is 8 m and width 3 m, then its perimeter is:

Perimeter = 2 × (8 + 3) = 22 meters

Let's imagine a rectangle:

8 m 3 m

Circle

The perimeter of a circle is called its circumference. It can be calculated using the diameter or radius (half of the diameter) from the number π (pi), which is approximately equal to 3.14159.

Circumference of a Circle = 2 × π × radius

Example:

If the radius of a circle is 7 m, then its circumference is:

Circumference = 2 × π × 7 ≈ 44 meters

Let's imagine a circle:

7 m

Understanding the area

Area is the amount of space inside a two-dimensional shape. Imagine you are coloring the inside of a shape; the area is the surface you will color. Area is measured in square units, such as square meters, square centimeters, or square feet.

Area of common shapes

Square

To find the area of a square, you multiply the length of one side by the length of the square.

Area of a Square = side × side = side 2

Example:

If one side of a square is 5 m, then its area is:

Area = 5 × 5 = 25 square meters

Rectangle

The area of a rectangle is found by multiplying its length by its width.

Area of a Rectangle = length × width

Example:

If the length of a rectangle is 8 m and width 3 m, then its area is:

Area = 8 × 3 = 24 square meters

Triangle

The area of a triangle can be found using a formula relating its base and height.

Area of a Triangle = 1/2 × base × height

Example:

If the base of a triangle is 6 m and height is 4 m, then its area is:

Area = 1/2 × 6 × 4 = 12 square meters

Circle

The area of a circle is calculated using its radius and the number π (pi).

Area of a Circle = π × radius 2

Example:

If the radius of a circle is 7 m, then its area is:

Area = π × 7 × 7 ≈ 154 square meters

Combined example: area and perimeter of a rectangle

Consider a garden that is in the shape of a rectangle 12 m long and 5 m wide. We want to find both the perimeter and the area.

For the perimeter:

Perimeter = 2 × (length + width) = 2 × (12 + 5) = 34 meters

For the area:

Area = length × width = 12 × 5 = 60 square meters

Practical applications

Understanding area and perimeter is necessary in many real-life situations. For example, if you are planning to build a fence around your garden, you will need to calculate the perimeter to know how much material to purchase for the fencing. Conversely, if you are laying or planting grass in your garden, you will need to know the area.

Conclusion

By understanding the simple concepts of perimeter and area, one can solve many practical problems related to measurement in real life. Whether you are planning to tile the floor, paint a room or build a swimming pool, knowing how to calculate area and perimeter will give you the measurements you need to get the job done efficiently.


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