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Class 7th Science
Class 7th Math
Online Class For 7th Standard Students (CBSE)
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Perimeter and Area Class 7 Notes: Chapter 11


  • Perimeter is the total length or total distance covered along the boundary of a closed shape

The perimeter of a Quadrilateral 


  • The area is the total amount of surface enclosed by a closed figure.

Areas of a closed figure

The perimeter of Square and Rectangle

  • Perimeter of a square = a + a + a + a = 4a, where a is the length of each side.

Square with side length ‘a’ units
  • Perimeter of a rectangle = l + l + b + b = 2(l + b), where l and b are length and breadth, respectively.

Rectangle with length ‘l’ units and breadth ‘b’ units

  • Area of each triangle = 12 (Area of the rectangle).
    =  12(length×breadth)
    =  12(10cm×5cm)
    =  25cm2

Area of a Triangle

  • Consider a parallelogram ABCD.
  • Draw a diagonal BD to divide the parallelogram into two congruent triangles.

Area of Triangle = 1/2 (base×height)
  • Area of triangle ABD = 1/2 (Area of parallelogram ABCD)

Area of triangle ABD  = 1/2 (b×h)

Conversion of Units

  • Kilometres, metres, centimetres, millimetres are units of length.
  • 10 millimetres = 1 centimetre
  • 100 centimetres = 1 metre
  • 1000 metres = 1 kilometre

Life of Pi

Terms Related to Circle

  • circle is a simple closed curve which is not a polygon.
  • A circle is a collection of points which are equidistant from a fixed point.

  • The fixed point in the middle is called the centre.
  • The fixed distance is known as radius.
  • The perimeter of a circle is also called as the circumference of the circle.

Introduction and Value of Pi

  • Pi (π)  is the constant which is defined as the ratio of a circle’s circumference (2πr) to its diameter(2r).

π= Circumference (2πr)/Diameter (2r)

  • The value of pi is approximately equal to 3.14159 or 22/7.

Problem Solving

Cost of Framing, Fencing

  • Cost of framing or fencing a land is calculated by finding its perimeter.
  • Example: A square-shaped land has length of its side 10m.
    Perimeter of the land = 4 × 10 = 40m
    Cost of fencing 1m = Rs 10
    Cost of fencing the land = 40 m × Rs 10 = Rs 400

Cost of Painting, Laminating

  • Cost of painting a surface depends on the area of the surface.
  • Example: A wall has dimensions 5m×4m.
    Area of the wall = 5m×4m=20m2
    Cost of painting 1m2 of area is Rs 20.
    Cost of painting the wall =20m2×Rs 20=Rs 400

Area of Mixed Shapes

  • Find the area of  the shaded portion using the given information.

Area of the shaded portion

Solution: Diameter of the semicircle = 10cm
Radius of semicircle = 5cm
Area of the shaded portion = Area of rectangle ABCD – Area of semicircle
Area of the shaded portion  = (l×b) − (πr2/2)
30×10 − (π×52/2)
300 − (π×25/2)
= (600 – 25π)/2
= (600 – 78.5)/2

260.7 cm2

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