Perimeter and Area Class 7 Notes: Chapter 11

Perimeter

  • Perimeter is the total length or total distance covered along the boundary of a closed shape.
    Perimeter of a Quadrilateral    
    The perimeter of a Quadrilateral    

Area

  • The area is the total amount of surface enclosed by a closed figure.
    Areas of 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.
The perimeter of Square and Rectangle
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
Rectangle with length ‘l’ units and breadth ‘b’ units

Area of Square & Rectangle

Area of square = 4a2

Here a is the length of each side

Square with the length of each side 'a' units
Square with the length of each side ‘a’ units

 

Area of rectangle = Length(l) × Breadth(b) = l×b

 

Area of rectangle = Length(l) × Breadth(b) = l×b
Rectangle with length ‘a’ units and breadth ‘b’ units

Area of a Parallelogram

Area of a Parallelogram

  • Area of parallelogram ABCD = (base×height)

Area of parallelogram ABCD  = (b×h)

Triangle as Part of Rectangle

  • The rectangle can be considered as a combination of two congruent triangles.
  • Consider a rectangle ABCD, it is divided into 2 triangles ACD and ABD.
    Triangle as Part of Rectangle
    Triangles as parts of Rectangle
  • 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 trinagles.

 

Area of a Triangle
Area of Triangle

 

  • Area of triangle ABD = 12 (Area of parallelogram ABCD)

12(base×height)

Area of triangle ABD  =  12(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

  • A 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.

Circle

  • 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.

Circumference of a Circle

  • The circumference of a circle ( C )  is the total path or total distance covered by the circle. It is also called a perimeter of the circle.

Circumference of a circle = 2×π×r,

where r is the radius of the circle.

Visualizing Area of a Circle

Area of Circle

  • Area of a circle is the total region enclosed by the circle.

Area of a circle = π×r2, where r is the radius 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 227.

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 = Rs10
    Cost of fencing the land = 40m × Rs10 = 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 Mixed Shapes
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×bπr22
300π×522
= 300π×252
= 60025π2
= 60078.52
= 260.7 cm2

1 Comment

  1. Every useful
    Thank you byjus
    Love you

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