Скачать или смотреть Class 6 Maths Chapter 6 Perimeter and Area | Perimeter

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Perimeter
Do you remember what the perimeter of a closed plane figure is?
Let us refresh our understanding!
The perimeter of any closed plane figure is the distance covered
along its boundary when you go around it once. For a polygon, i.e.,
a closed plane figure made up of line segments, the perimeter is
simply the sum of the lengths of its all sides, i.e., the total distance
along its outer boundary.
The perimeter of a polygon = the sum of the lengths of its all sides.
Let us revise the formulas for the perimeter of rectangles, squares,
and triangles.
Perimeter of a Rectangle
Consider a rectangle ABCD whose length and breadth are 12 cm and
8 cm, respectively. What is its perimeter?
Perimeter of the rectangle = Sum of the lengths of its four sides
From this example, we see that—
Perimeter of a rectangle = length + breadth + length + breadth.
Perimeter of a rectangle = 2 × (length + breadth).
The perimeter of a rectangle is twice the sum of its length and breadth.
Perimeter of a Square
Debojeet wants to put coloured tape all around
a square photo frame of side 1m as shown.
What will be the length of the coloured tape
he requires? Since Debojeet wants to put the
coloured tape all around the square photo
frame, he needs to find the perimeter of the
photo frame.
Thus, the length of the tape required =
perimeter of the square
= sum of the lengths of all four sides of the square
= 1 m + 1 m + 1 m + 1 m = 4 m.
Now, we know that all four sides of a square are equal in length.
Therefore, in place of adding the lengths of each side, we can simply
multiply the length of one side by 4.
Thus, the length of the tape required = 4 × 1 m = 4 m.
From this example, we see that
Perimeter of a square = 4 × length of a side.
The perimeter of a square is quadruple the length of its side.
Perimeter of a Triangle
Consider a triangle having three given sides of
lengths 4 cm, 5 cm and 7 cm. Find its perimeter.
Perimeter of the triangle = 4 cm + 5 cm + 7 cm
= 16 cm.
Perimeter of a triangle = sum of the lengths of its three sides.
Example: Akshi wants to put lace all around a
rectangular tablecloth that is 3 m long and 2 m
wide. Find the length of the lace required.
Solution
Length of the rectangular table cover = 3 m.
Breadth of the rectangular table cover = 2 m.
Akshi wants to put lace all around the
tablecloth.
Therefore, the length of the lace required will be the perimeter of the
rectangular tablecloth.
Now, the perimeter of the rectangular tablecloth = 2 × (length + breadth)
= 2 × (3 m + 2 m) = 2 × 5 m = 10 m.
Hence, the length of the lace required is 10 m.
Example: Find the distance travelled by Usha if she takes three rounds of
a square park of side 75 m.
Solution
Perimeter of the square park = 4 × length
of a side = 4 × 75 m = 300 m.
Distance covered by Usha in one
round = 300 m.
Therefore, the total distance travelled by
Usha in three rounds = 3 × 300 m = 900 m.