NCERT 6TH CLASS MATHEMATICS CHAPTER MENSURATION

PERIMETER

The perimeter of a closed figure is the length of the boundary of the figure.
we find perimeter when we
   (a) walk around a garden.
   (b) want to know the cost of fencing the fleid.
   (c) build a boundary wall around our house.
   (d) put a lace around a table cover.
   (e) want to know the wood stick required to make a picture frame.
The perimeter of this pentagon is sum of the sides
AB + BC + CD + DE + EA = 1cm + 2cm + 3cm + 5cm + 4cm = 15cm
 
 

Perimeter of Rectangle:

The perimeter of a rectangle is the sum of all its sides.
The opposite sides of rectangle are equal. If one side, say the longer side, is l unit and the shorter side is b unit, then perimeter = twice the length + twice the breadth.
Perimeter = length + breadth + length + breadth = 2(length) + 2(breadth) = 2(length + breadth)
 
= 2(l + b) where l = length 
b = breadth

Perimeter of a square :

A square is a special rectangle with all the four sides equal. If one side of a square measures a unit, we can say that both the length and the breadth are a unit each.
Perimeter of a square = 2(l + b)
= 2(a + b)
= 2 × 2a
= 4a
= 4 times the side
The perimeter of a square is equal to four times the length of its sides.

Perimeter of a triangle :

 
perimeter = a + b + c

Perimeter of an equiliateral triangle :

A triangle with all sides equal is called an equilateral triangle. If the length of one side of an equilateral triangle is a units, its perimeter will be side + side + side = a + a + a + 3a
In general, if the sides of a polygon are equal, that is, if it is a regular polygon, its perimeter will be the product of the length of its side with the number of sides.
Perimeter of a regular pentagon = 5a units
Perimeter of a regular hexagon = 6a units
Perimeter of a regular octagon = 8a units
where a is the length of one side.
 
Ex. Find the perimeter of rectangle having length 12cm and breadth 8cm.
Sol. Length = 12cm
       Breadth = 8cm
       Perimeter of rectangle= 2(length + breadth)
      = 2(12 + 8)
      = 40cm
 
Ex. Find the side of square having perimeter 28 cm
Sol. Perimeter of square = 4 × side
      Side =Perimeter/4=28/4  = 7cm
 
Ex. Find the cost of fencing a square park of side 300 m at the rate Rs. 25 per meter
Sol. Perimeter of square = 4 × side
      = 4 × 300 = 1200 m
     Cost of fencing = Per
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