NEETClass 11thClass 12thClass 12th PlusJEEClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thOnline CoursesDistance LearningInternational OlympiadNEETClass 11thClass 12thClass 12th PlusJEE (Main+Advanced)Class 11thClass 12thClass 12th PlusJEE MainClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thKCET/MHT-CETKCETMHT-CETNEET20262025202420232022JEE20262025202420232022Class 6-1020262025JEE MainPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DatePercentile PredictorAnswer KeyCounsellingEligibilityExam PatternJEE MathsJEE ChemistryJEE PhysicsJEE AdvancedPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateAnswer KeyEligibilityExam PatternRank PredictorNEETPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateCollege PredictorAnswer KeyRank PredictorCounsellingEligibilityExam PatternBiologyNCERT SolutionsClass 6Class 7Class 8Class 9Class 10Class 11Class 12TextbooksCBSEClass 12Class 11Class 10Class 9Class 8Class 7Class 6SubjectsSyllabusNotesSample PapersQuestion PapersICSEClass 10Class 9Class 8Class 7Class 6State BoardBiharKarnatakaMadhya PradeshMaharashtraTamilnaduWest BengalUttar PradeshOlympiadMathsScienceEnglishSocial ScienceNSOIMONMTCTALLENTEXASATInstant Online ScholarshipAIOT(NEET)ALLEN for SchoolsAbout ALLENBlogsNewsCareersRequest a call backBook a demo
CBSE Notes Class 6 Maths Chapter 6 Perimeter and Area
Perimeter is the total distance around the edge of a shape. To find it, we add the lengths of all the sides. Area is the amount of space inside a shape, measured in square units like cm² or m². To calculate area, we use different formulas depending on the shape. For example, the area of a rectangle is length × width, and the perimeter is the sum of all sides. Understanding these concepts helps us solve real-life problems like measuring land or building materials.
1.0What is Perimeter?
The Perimeter of a shape is the total length of the boundary or the distance around the shape.
To find the perimeter, you simply add up the lengths of all the sides of the shape. Let’s look at some common shapes and how we calculate their perimeters
Perimeter of a Rectangle
A Rectangle is a shape with four sides, where opposite sides are equal in length. To find the perimeter of a rectangle, we use this formula:
Perimeter of Rectangle = 2 × (Length + Breadth)
For example, if a rectangle has a length of 8 cm and a breadth of 5 cm, the perimeter will be:
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm
Perimeter of a Square
A Square is a special kind of rectangle where all four sides are equal in length. To calculate the perimeter of a square, you simply multiply the length of one side by 4:
Perimeter of Square = 4 × Side
For example, if one side of a square is 5 cm, the perimeter will be:
Perimeter = 4 × 5 = 20 cm
Perimeter of a Triangle
A Triangle has three sides. To find the perimeter of a triangle, simply add up the lengths of all three sides:
Perimeter of Triangle = a + b + c
For example, if a triangle has sides measuring cm, 8 cm, and 10 cm, the perimeter will be:
Perimeter = 5 + 8 + 10 = 23 cm
Perimeter of a Regular Polygon
A Regular Polygon is a polygon in which all sides are equal in length. To find the perimeter of a regular polygon, you multiply the length of one side by the total number of sides:
Perimeter of Regular Polygon = Number of sides × Length of one side
For example, for a regular hexagon (a polygon with 6 sides) with each side measuring 2 cm, the perimeter will be:
Perimeter = 6 × 2 = 12 cm
Perimeter of an Equilateral Triangle
An Equilateral Triangle is a triangle where all three sides are of equal length. To find its perimeter, simply multiply the length of one side by 3:
Perimeter of Equilateral Triangle = 3 × Side
For example, if one side of an equilateral triangle is 4 cm, the perimeter will be:
Perimeter = 3 × 4 = 12 cm
2.0What is Area?
While Perimeter measures the distance around the boundary of a shape, Area measures the amount of space inside the shape. It tells us how much surface a shape covers. We measure area in square units like square centimetres (cm²), square meters (m²), or square inches (in²).
Now, let’s look at how to calculate the area of some common shapes:
Area of a Triangle
To calculate the Area of a Triangle, we use the formula:
For example, if a triangle has a base of 6 cm and a height of 4 cm, the area will be:
Also Read :- Area of Equilateral Triangle
Key Concepts to Remember
- Perimeter: The perimeter of a closed figure is the total distance around its boundary. For a polygon, add the lengths of all its sides to find the perimeter.
- Perimeter of a rectangle: Opposite sides of a rectangle are equal. Its perimeter is twice the sum of its length and breadth.
- Perimeter of a square: All four sides of a square are equal. Multiply the length of one side by 4 to find its perimeter.
- Perimeter of a triangle: Add the lengths of its three sides. For example, a triangle with sides of 4 cm, 5 cm and 7 cm has a perimeter of 16 cm.
- Perimeter of a regular polygon: A regular polygon has all sides and all angles equal. Its perimeter can be found by adding the lengths of all its sides. For equal sides, multiply one side's length by the number of sides.
- Area: Area is the amount of region enclosed by a closed figure. It measures the surface covered by a shape.
- Area of a rectangle: Multiply its length by its breadth to calculate the area.
- Area of a square: Multiply the length of one side by itself to calculate the area.
- Area using square grids: A shape's area can be identified by counting the unit squares it covers. In case of partially covered squares, follow the textbook's counting conventions.
- Area of a triangle: A rectangle divided along its diagonal forms two triangles of equal area. Each triangle has half the area of the rectangle.
- Perimeter and area are different: Perimeter measures the boundary length, whereas area measures the enclosed region. Two shapes can have the same area but different perimeters.
- Units of measurement: Perimeter is expressed in linear units, such as centimetres and metres. Area is expressed in terms of square units, such as square centimetres and square metres.
3.0Important Formulas Perimeter and Area
Perimeter formulas
Here, P represents perimeter, l represents length, b represents breadth, and s represents side length.
Examples:
- Rectangle with length 12 cm and breadth 8 cm: P=2(12+8)=40cm.
- Square with side 5 m: P=45=20m.
- Equilateral triangle with side 6 cm: P=36=18cm.
Area formulas and rules
Examples:
- Rectangle with length 5 m and breadth 4 m: A=54=20m2.
- Square with side 3 m: A=33=9m2.
- A floor has an area of 20 m² and a carpet covers 9 m². The uncovered area is 20-9=11m2.
Remember: the numerical value of a measurement is incomplete without the correct unit. Do not write square units for perimeter or ordinary linear units for area.
4.0Learning Guide for Class 6 Maths Perimeter and Area - Chapter 6
- Finding the perimeter of everyday objects: Imagine putting lace around a rectangular tablecloth. If it is 3 m long and 2 m wide, calculate 2(3+2)=10m. Therefore, 10 m of lace is required.
- Calculating distance over multiple rounds: Find the perimeter of the track first, then multiply it by the number of rounds. For a square park with a side of 75 m, one round is 475=300m. Three rounds cover 3300=900m.
- Working backwards from perimeter: If a rectangle has a perimeter of 14 cm and a breadth of 2 cm, then 14=2(l+2). Dividing by 2 gives l+2=7, so the length is 5 cm.
- Understanding regular polygons: Compare squares, equilateral triangles and regular pentagons. Since the sides of each regular polygon are equal, use the number of sides and the length of one side to calculate the perimeter.
- Exploring how shapes change: Cut a rectangular paper into equal parts and rearrange them in different ways. Compare the new boundaries to understand how changing a shape can change its perimeter.
- Finding area using grids: Treat each complete unit square as one square unit. Ignore portions smaller than half a square, count portions larger than half as one square unit, and count an exact half-square as half a square unit.
- Comparing area and perimeter: Make different connected shapes using nine unit squares. Compare their boundary lengths for fixed total area. This shows that equal areas do not always give equal perimeters.
- Finding the area of combined shapes: Divide a complicated figure into rectangles and triangles. Calculate the area of each part and add the results. If a region is excluded, subtract its area from the total.
- Understanding triangle area: Draw a diagonal across a rectangle and cut along it. The two resulting triangles have equal areas, each equal to half the rectangle's area.
- Using tangram pieces: Compare shapes by placing the textbook's tangram pieces over one another or combining them. Pieces that cover exactly the same region have equal areas, even when their outlines differ.
5.0Explore Chapter-wise Class 6 Maths Notes
6.0Additional Study Materials for Class 6 Maths
7.0Find the Right Study Resources for Class 6
8.0Benefits of CBSE Notes for Class 6 Maths Chapter 6 - Perimeter and Area
- Improved Problem-Solving Skills: By studying well-crafted CBSE Notes for Class 6 Maths and the included examples, you can develop a better understanding of how to approach and solve various problems related to perimeter and area.
- Conceptual Clarity: CBSE Notes can provide additional explanations or alternative perspectives that might not be immediately clear from the NCERT Solutions textbook alone, leading to deeper conceptual clarity.
- Time-Saving: Instead of searching through the entire chapter for specific information, well-organised CBSE Notes for Class 6 provide all the essential details in one place, saving you valuable study time.
- Building a Strong Foundation: A solid understanding of perimeter and area in CBSE Class 6 forms a crucial foundation for more advanced geometry concepts in higher classes. Good notes can help you build this strong base.
- Self-Assessment: Some notes might include practice questions or summaries that allow you to quickly assess your understanding of the chapter.