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CBSE Notes
Class 7
Maths
Chapter 9 Perimeter And Area

CBSE Notes Class 7 Maths Chapter 9 Perimeter and Area

Chapter 9 of Class 7 Maths introduces the concepts of Perimeter and Area. Mensuration is the process or art of measuring, applied to anything that can be measured. In geometry, perimeter refers to the total boundary length of a closed figure, while area is the amount of surface covered by a shape. A planar region, which has two dimensions (length and breadth), is measured in terms of its area. These concepts are essential for solving practical problems like determining the length of fencing required or the amount of material needed for flooring.

1.0Triangle

  1. Perimeter of a Triangle

Perimeter = Sum of Sides = a + b +c 

Triangle

  1. Area of a Triangle:

 Area =21​× base × height 

Area of a triangle

  1. Area of an Equilateral Triangle:

 Area =43​​a2,where (a) is the side length.

Equilateral triangle

NOTE: ALSO WRITE h in equilateral Triangle. 

  1. Median/Altitude/Angle Bisector: For an equilateral triangle, the median (or altitude) is:  Median =23​​a
  2. Circumcircle and Incircle: If (R) is the radius of the circumcircle and (r) is the radius of the incircle: R = 2r
  3. Perimeter of an Equilateral Triangle: Perimeter =3a
  4. Area of an Isosceles Triangle: Area =4b4a2−b2​​

Isosceles triangle

  1. Height of an Isosceles Triangle: Height =a2−(4b2​)​

2.0Quadrilateral

Area of Any Quadrilateral: The area is the sum of the areas of two triangles formed by a diagonal.

  1. If diagonals are inside the quadrilateral

 Area =21​× diagonal ×( Sum of the two perpendiculars )

A=21​×d×(P1​+P2​) 

Quadrilateral

  1. If the diagonal falls outside the figure, then

 Area of the quadrilateral =21​× diagonal ×( difference of the perpendiculars )

 Area =21​×d×(P1​−P2​)

Quadrilaterals

3.0Square

A square is a quadrilateral where:

  1. All sides are equal: AB = BC = CD = DA = a 
  2. Diagonals are equal: AC = BD = d 
  3. Diagonals bisect each other at 90°, with a2=2d2​ 

Perimeter of a Square:

 Perimeter =4× side =4a

Area of a Square:

  •  Area = side 2=a2
  •  Area =2 diagonal ​=2d2​

Diagonal of a square =2​(sides)

Square

4.0Rectangle

A rectangle is a quadrilateral whose, 

  1. Opposite sides equal and parallel: AB=CD=ℓ (length), AD = BC = b (breadth)
  2. Equal diagonals that bisect each other: AC = BD = d 
  3. All angles ∠A=∠B=∠C=∠D=90∘

Diagonal relation:

d2=l2+b2

Area of a Rectangle:

 Area = length × breadth =l×b

Perimeter of a Rectangle:

 Perimeter =2 (length + breadth )=2(l+b)

Rectangle

5.0Parallelogram

A parallelogram is a quadrilateral with:

  1. Opposite sides equal and parallel: AB = CD = b, AD = BC = a 
  2. Diagonal AC = d 
  3. Height h between bases

parallelogram area

  1. Perimeter of a Parallelogram:

 Perimeter =2( sum of adjacent sides )=2(a+b)

  1. Area of a Parallelogram:

 Area = base × height =b×h

 Area =ah1​=bh2​

parallogram

Also Read: Properties of a Parallelogram

6.0Trapezium

  1. Area of a Trapezium:

 Area =21​( sum of parallel sides )×( perpendicular distance between them )

 Area =21​(a+b)h

Trapezium

Also Read: Area of Trapezium

7.0Circle

A circle consists of all points in a plane equidistant from a fixed point called the center (O).

The distance from the center to any point on the circle is the radius (r). 

Any line passing through the center and ending at both sides of the circumference is called the diameter (AC').

Circle

8.0Circumference and Area of the Circle

The circumference (C) is the perimeter of a circle, and the area (A) is the space it encloses.

  • Radius: OB = r 
  • Diameter: AC' = d = 2r 

Formulas:

  • Circumference: C=2πr=πd
  • Area: A=πr2
  • Correlation: A=4πC2​

Also Read: Area of a Circle

9.0Semicircle

Area of semicircle =2πr2​

Perimeter of semicircle (including the straight edge) = πr + 2r

Semicircle

10.0Pathway 

  1. Pathway Outside the Plot: 

For a rectangular plot ABCD with length ℓ and breadth b , and a pathway of width W  outside the plot, the area of the pathway is:  

A0​=2W(ℓ+b+2W)

Pathway Outside the Plot for rectangle

  1. Pathway Inside the Plot:  

If the pathway is inside the plot, the area is:  

A1​=2W(ℓ+b−2W)

Pathway Inside the Plot or rectangle

  1. Parallel Paths:   

For the same rectangular plot with parallel paths SU and TV, each of width W, the area of the two parallel paths is:  

A=W(ℓ+b−W)

parallel paths

11.0Circular Pathway

  1. Pathway Outside the Circle:

For a circle ABC with radius r and a pathway of width W outside it, the area of the pathway is:  

 Area =πW(2r+W)

Pathway Outside the Circle

  1. Pathway Inside the Circle:

For a pathway of width W inside the circle, the area is:  

 Area =πW(2r−W)

Pathway Inside the Circle

Circular Ring:

If R and r are the radii of the outer and inner circles respectively, with W = R - r (width of the ring), the area of the ring is:  

 Area =π(R2−r2)=π(R+r)W

Circular Ring

12.0Key Features of Class 7 Maths Chapter 9: Perimeter and Area

  • Concepts related to finding the area of trapeziums, rhombuses, and polygons.
  • Step-by-step methods to calculate the circumference and area using π (pi).
  • Content structured as per the latest CBSE curriculum and exam patterns.
  • Summary points and key formulas provided for fast revision before exams.

13.0Sample Questions on Perimeter and Area

  1. How do you find the perimeter of a rectangle?  

Add the lengths of all sides or use P=2(ℓ+b).

  1. How do you find the area of a circle?  

Use A=πr2, where r is the radius.

Chapter-wise CBSE Notes for Class 7 Maths:

Class 7 Maths Chapter 1 - Integers Notes

Class 7 Maths Chapter 2 - Fractions and Decimals Notes

Class 7 Maths Chapter 3 - Data Handling Notes

Class 7 Maths Chapter 4 - Simple Equations Notes

Class 7 Maths Chapter 5 - Lines And Angles Notes

Class 7 Maths Chapter 6 - The Triangles and its Properties Notes

Class 7 Maths Chapter 7 - Comparing Quantities Notes

Class 7 Maths Chapter 8 - Rational Numbers Notes

Class 7 Maths Chapter 9 - Perimeter And Area Notes

Class 7 Maths Chapter 10 - Algebraic Expressions Notes

Class 7 Maths Chapter 11 - Exponents And Powers Notes

Class 7 Maths Chapter 12 - Symmetry Notes

Class 7 Maths Chapter 13 - Visualising Solid Shapes Notes


Chapter-wise NCERT Solutions for Class 7 Maths:-

Chapter 1: Integers

Chapter 2: Fractions and Decimals

Chapter 3: Data Handling

Chapter 4: Simple Equations

Chapter 5: Lines and Angles

Chapter 6: The Triangle and its Properties

Chapter 7: Comparing Quantities

Chapter 8: Rational Numbers

Chapter 9: Perimeter and Area

Chapter 10: Algebraic Expressions

Chapter 11: Exponents and Powers

Chapter 12: Symmetry

Chapter 13: Visualising Solid Shapes

Frequently Asked Questions

The perimeter is the total length around the boundary of a closed figure.

The area is the amount of space enclosed within a shape.

Perimeter measures the boundary length, while area measures the space within.

Yes, a shape’s perimeter and area vary based on its size and dimensions.

They are used in construction, fencing, flooring, and landscaping.

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