NCERT Book Class 6 Maths Perimeter and Area PDF Download

Chapter 6: Perimeter and Area

6.1 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
= AB + BC + CD + DA
= AB + BC + AB + BC
= 2 \times AB + 2 \times BC
= 2 \times (AB + BC)
= 2 \times (12 cm + 8 cm)
= 2 \times (20 cm)
= 40 cm.

[Figure: Rectangle ABCD with length 12 cm and breadth 8 cm, See in your textbook]

From this example, we see that -
Perimeter of a rectangle = length + breadth + length + breadth.
Perimeter of a rectangle = 2 \times (length + breadth).
The perimeter of a rectangle is twice the sum of its length and breadth.

Teacher's Note

When finding the perimeter of a rectangle, remember that opposite sides are equal: if one length is 12 cm, the opposite side is also 12 cm. This is why we multiply by 2 instead of adding four different numbers. Check your formula: \( P = 2 \times (l + b) \) uses length and breadth only once each, then doubles them.

Perimeter of a square

Debojeet wants to put coloured tape all around a square photo frame of side 1 m 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.

[Figure: A square with side 1 m, See in your textbook]

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 \times 1 m = 4 m.

From this example, we see that
Perimeter of a square = 4 \times 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.

[Figure: Triangle with sides 4 cm, 5 cm, and 7 cm, See in your textbook]

Perimeter of a triangle = sum of the lengths of its three sides.

Example

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 \times (length + breadth)
= 2 \times (3 m + 2 m)
= 2 \times 5 m = 10 m.
Hence, the length of the lace required is 10 m.

Teacher's Note

Read the problem carefully to identify what shape you have and what the question is asking for. In this example, "put lace all around" means you need the perimeter, not the area. Always match the formula to what the problem is asking: around the edge means perimeter; covering the surface means area.

Example

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 \times length of a side = 4 \times 75 m = 300 m.
Distance covered by Usha in one round = 300 m.
Therefore, the total distance travelled by Usha in three rounds = 3 \times 300 m = 900 m.

[Figure: A square park with a person walking around it, See in your textbook]

Key Points

• The perimeter of any closed plane figure is the total distance around its boundary, found by adding the lengths of all its sides.
• For a rectangle with length \( l \) and breadth \( b \), the perimeter is \( 2 \times (l + b) \).
• For a square with side \( s \), the perimeter is \( 4 \times s \).
• For a triangle with sides \( a \), \( b \), and \( c \), the perimeter is \( a + b + c \).
• When a problem asks you to go "around" a shape, find the perimeter; use formulas carefully and include units in your answer.

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