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    

For More Information On Perimeter, Watch The Below Video.


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Area

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

For More Information On Visualizing Area, Watch The Below Video.


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

To know more about Perimeter Formula’s of All geometrical Figures, visit here.

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) √ó Breadth(b) = l√ób

 

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

Area of a Parallelogram

Area of a Parallelogram

  • Area of parallelogram ABCD =¬†(base√óheight)

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 triangles.
Area of a Triangle
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)

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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.

For More Information On Terms Related To Circle, Watch The Below Video.


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√óŌÄ√ór,

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 = ŌÄ√ór2, where r is the radius of the circle.

For More Information On Area Of Circle, Watch The Below Video.


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Introduction and Value of Pi

  • Pi (ŌÄ)¬†¬†is the constant which is defined as the ratio of a circle‚Äôs circumference¬†(2ŌÄr)¬†to its¬†diameter(2r).

ŌÄ= Circumference (2ŌÄr)/Diameter (2r)

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

For More Information On The Value Of Pi, Watch The Below Video.


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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 √ó 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√ó4m.
    Area of the wall = 5m√ó4m=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√ób)¬†‚ąí (ŌÄr2/2)
=¬†30√ó10¬†‚ąí (ŌÄ√ó52/2)
= 300¬†‚ąí¬†(ŌÄ√ó25/2)
= (600 – 25ŌÄ)/2
= (600 – 78.5)/2

= 260.7 cm2

1 Comment

  1. Every useful
    Thank you byjus
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