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 ↓


Perimeter of Plane Figures


The concept of perimeter is an essential part of geometry and measurement. Understanding the perimeter of plane figures helps us solve real-world problems such as designing a garden, enclosing a piece of land or framing a picture, etc. In simple terms, perimeter is the total distance around the edge of a two-dimensional figure. It gives us an idea of how much boundary or border a figure encloses.

Definition of perimeter

The perimeter is the continuous line forming the boundary of a closed plane figure. Imagine you are walking in a park; the distance you will cover to come back to the same point will be the perimeter of the park.

Understanding plane figures

A plane figure is a two-dimensional shape that lies entirely on a flat surface. Common examples include circles, triangles, rectangles, and squares. Each of these shapes has its own method for calculating the perimeter.

Calculating the perimeter of general plane figures

Perimeter of a rectangle

A rectangle is a plane figure whose opposite sides are equal and parallel. The formula for calculating the perimeter of a rectangle depends on its length and width:

    P = 2(length + width)

Here, P represents the perimeter, while length and width are the measurements of the sides of the rectangle.

Example: If the length of a rectangle is 6 cm and width is 4 cm, then its perimeter is: 
P = 2(6 + 4) = 2 x 10 = 20 cm

Perimeter of a square

A square is a special rectangle in which all four sides are equal. The formula for the perimeter of a square can be simplified because all its sides are equal:

    P = 4 x side

Here, P represents the perimeter, and side is the length of one side of the square.

Example: If one side of a square is 5 cm, then its perimeter is: 
P = 4 x 5 = 20 cm

Perimeter of a triangle

A triangle has three sides, and its perimeter is the sum of all sides. The general formula is:

    P = A + B + C

Here, P represents the perimeter and A, B, and C are the lengths of the sides of the triangle.

Example: If the sides of a triangle are 6 cm, 7 cm and 9 cm, then the perimeter is: 
P = 6 + 7 + 9 = 22 cm

Circumference of a circle

The perimeter of a circle is called the circumference. The formula to calculate the circumference is pi (π), which is approximately 3.14159. The formula for the circumference of a circle is:

    C = 2πr

Here, C is the circumference of the circle and r is the radius.

Example: If the radius of a circle is 3 cm, then what will be its perimeter (circumference): 
C = 2 x 3.14159 x 3 ≈ 18.85 cm

Visual example

Rectangle

Length Width

Square

Side

Triangle

A B C

Circle

R

Understanding units of perimeter

When calculating the perimeter, units are an essential aspect to consider. The unit of measurement is determined by the unit used for the length of the sides. For example, if the sides of the shape are measured in centimeters, the perimeter will also be in centimeters. Common units include millimeters (mm), centimeters (cm), meters (m), and kilometers (km).

Reinforcing understanding through word problems

Word problem 1

Suppose Mr. Brown wants to fence his garden, which is rectangular in shape. The length of the garden is 40 m, and the width is 15 m. Calculate the total length of the fence that Mr. Brown will need.

Solution: Using the perimeter formula of a rectangle:

    P = 2(length + width)
      = 2(40 + 15)
      = 2 x 55
      = 110 meters

Mr. Brown will need 110 meters of fencing.

Word problem 2

Emma is putting ribbon around a square cake. If one side of the cake is 25 cm long, how much ribbon will Emma need?

Solution: Using the perimeter formula of a square:

    P = 4 x side
      = 4 x 25
      = 100 cm

Emma needs 100 cm of ribbon.

Extending the ideas: Complex shapes

Many times, we come across shapes that are combinations of other simple shapes. Imagine a flower garden that includes a rectangular path and a circular pond. In such cases, the total perimeter is the sum of the perimeters of each individual shape. Each part of the shape will use its respective perimeter formula.

Conclusion

Understanding how to find the perimeter of various plane figures is a practical and valuable skill. It helps students understand the dimensions and limitations of various shapes and can be applied to solve real-world problems. With practice, calculating perimeter becomes intuitive and simple.


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Perimeter of Plane Figures

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