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

 

 

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

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 = a + b + c

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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