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 ↓


Perimeter of Polygons


In the world of mathematics, there are many concepts that help us understand shapes, sizes, and the mathematical relationships between them. One such important concept is the measurement of perimeter, especially with regard to polygons. A polygon is, first of all, a flat, two-dimensional shape with straight sides. Some common examples of polygons include triangles, quadrilaterals, pentagons, hexagons, etc.

Definition of perimeter

The perimeter of any polygon is defined as the total length of its boundary or the sum of the lengths of all its sides. When you walk along the edge of a shape, you travel a distance that can be described as the perimeter. It is like a running track around a playground; if you walk around it once, you have traveled the perimeter.

Perimeter of general polygons

Let's look at how to calculate the perimeter for some common polygons:

1. Triangle

A triangle is a three-sided polygon. The perimeter of a triangle is simply the sum of its three sides. If the sides of the triangle are a, b and c, then the perimeter P is calculated as:

P = A + B + C

For example, consider a triangle with sides 3 cm, 4 cm and 5 cm. The perimeter will be:

P = 3 cm + 4 cm + 5 cm = 12 cm

2. Quadrilateral

A quadrilateral is a four-sided polygon. The perimeter of a quadrilateral is the sum of its four sides. If the sides are a, b, c and d, then the perimeter P is:

P = A + B + C + D

For example, for a rectangle with opposite sides 6 cm and 4 cm, we calculate the perimeter as follows:

P = 6 cm + 4 cm + 6 cm + 4 cm = 20 cm

3. The pentagon

A pentagon is a five-sided polygon. To determine the perimeter, add up all five sides:

P = A + B + C + D + E

For a regular pentagon, all sides are equal, so if each side measures 7 cm:

P = 5 × 7 cm = 35 cm

Calculating the perimeter: More visual examples

Triangle example

C a=3cm b=4cm

To find the perimeter of this triangle with sides a = 3cm, b = 4cm, and c = 5cm:

P = a + b + c = 3cm + 4cm + 5cm = 12cm

Quadrilateral example

b=100cm A=180cm d=100cm C=180cm

To calculate the perimeter:

P = a + b + c + d = 180 cm + 100 cm + 180 cm + 100 cm = 560 cm

Regular pentagon example

102cm 102cm 102cm 102cm 102cm

For a regular pentagon with each side measuring 102 cm:

P = 5 × 102cm = 510cm

Some important tips for calculating perimeter

  • Label the sides: Always make sure to label the sides of the polygons when you're faced with a problem. This will help ensure that you include all sides in your calculations.
  • Check for regularity: If the polygon is regular, all sides are equal, making the calculation simple by multiplying one side by the number of sides.
  • Use units: Always include appropriate units in your answer (eg. cm, m, etc.), as this helps in understanding the scale of measurement.

Why is perimeter important?

Understanding perimeter is important in real-life applications. It is used in fields such as architecture and planning where boundaries must be clearly defined. For example, in gardening, perimeter helps determine how much fencing material is needed to enclose a garden. Also, perimeter calculations are necessary for arranging decorations or furniture at an event.

Practice problems with solutions

  1. The sides of a triangle are 7 cm, 9 cm and 12 cm. What is the perimeter?

    P = 7 cm + 9 cm + 12 cm = 28 cm

  2. The sides of a rectangle are 8 cm and 3 cm. Find its perimeter.

    P = 8 cm + 3 cm + 8 cm + 3 cm = 22 cm

  3. Find the perimeter of a square with side 5 cm.

    P = 4 × 5 cm = 20 cm

  4. The measure of each side of a pentagon is 8 cm. What is the perimeter?

    P = 5 × 8 cm = 40 cm

Investigating complex polygons

Perimeter becomes more challenging with complex polygons - those that are not standard geometric shapes. In such cases, divide the polygon into known shapes, calculate the perimeter of each segment, and sum them for the total.

Conclusion

Mastering the concept of calculating the perimeter of polygons depends on a clear understanding of how to correctly add side lengths, recognize shapes, and apply formulas appropriately. With thoughtful practice, the process of calculating the perimeter of polygons becomes an integral part of solving more complex geometric problems and real-world applications.


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Perimeter of Polygons

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