Class 6 — Mathematics (NCERT)
Mensuration: Perimeter and Area of Rectangles and Squares
Class 6
- ✓By the end of this lesson students will be able to define perimeter and area.
- ✓By the end of this lesson students will be able to calculate the perimeter of rectangles and squares.
- ✓By the end of this lesson students will be able to calculate the area of rectangles and squares.
- ✓By the end of this lesson students will be able to apply the concepts of perimeter and area to solve real-life problems.
- ✓By the end of this lesson students will be able to understand and use appropriate units for perimeter and area.
Key concepts
The perimeter of a closed figure is the total distance covered along its boundary. To find the perimeter, we add the lengths of all the sides of the figure. The unit of perimeter is the same as the unit of length (e.g., centimetre (cm), metre (m), kilometre (km)).
The area of a closed figure is the measure of the surface enclosed by its boundary. It tells us how much space a flat shape occupies. The unit of area is a square unit (e.g., square centimetre (sq cm or cm²), square metre (sq m or m²), square kilometre (sq km or km²)).
It is crucial to use appropriate units. For perimeter, if lengths are in cm, perimeter is in cm. If lengths are in m, perimeter is in m. For area, if lengths are in cm, area is in sq cm. If lengths are in m, area is in sq m. Always remember to write the correct units with your answer.
Key facts to remember
- 1Perimeter is the total length of the boundary of a closed figure.
- 2Area is the measure of the surface enclosed by a closed figure.
- 3Perimeter of a rectangle = 2 × (length + breadth).
- 4Area of a rectangle = length × breadth.
- 5Perimeter of a square = 4 × side.
- 6Area of a square = side × side.
- 7Units for perimeter are linear (e.g., cm, m).
- 8Units for area are square units (e.g., sq cm, sq m).
Worked examples
Example 1
Find the perimeter of a rectangular park whose length is 150 m and breadth is 80 m.
Answer
The perimeter of the rectangular park is 460 m.
Example 2
A square field has a side of 60 m. Find its area.
Answer
The area of the square field is 3600 sq m.
Remember to use square units for area.
Example 3
The perimeter of a rectangular sheet of paper is 100 cm. If the length is 35 cm, find its breadth.
Answer
The breadth of the rectangular sheet of paper is 15 cm.
Common mistakes
- ✗Confusing the formulas for perimeter and area.
- ✗Using linear units (e.g., cm) for area instead of square units (e.g., sq cm).
- ✗Forgetting to include units in the final answer.
- ✗Adding only two sides for perimeter of a rectangle instead of all four, or using (l+b) instead of 2(l+b).
- ✗Multiplying by 2 for area instead of perimeter.
Exam tips
- ★Always read the question carefully to determine whether perimeter or area is required.
- ★Draw a rough diagram of the shape if it helps visualise the problem.
- ★Write down the given values and the correct formula before starting calculations.
- ★Show all steps clearly and neatly, as partial marks are often awarded for correct methods.
- ★Double-check your calculations and ensure the final answer includes the correct units.
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