NCERT 6TH CLASS MATHEMATICS CHAPTER MENSURATION
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
= 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)
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