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Avneet buys 9 square paving slabs, each with a side of 1/2 m. He lays them in the form of a square.
(a) What is the perimeter of his arrangement [Fig 10.7(i)]?
(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [(Fig 10.7 (ii)]?
(c) Which has greater perimeter?
(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)

Solution:

We will be calculating the perimeter of each of the given shapes.

(a) Side of each small square paving slab bought by Avneet = 1/2 m

According to the arrangement shown in Fig 10.7(i),

Each Side of the whole square = 3 × side of the small square paving slab [Since, the whole square is made up of 9 small square paving slabs]

⇒ 3 × 1/2 = 3/2 m

Perimeter of the whole Square = 4 × Side

⇒ 4 × 3/2

⇒ 2 × 3 = 6 m

Therefore, 6 m is the perimeter of the square shown in Fig 10.7(i).

(b) Perimeter of the cross figure shown in Fig 10.7 (ii) = 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1

= 10 m

Therefore, the perimeter of Shari's arrangement is10 m.

(c) Second figure that is Fig 10.7 (ii) has a greater perimeter.

(d) If all of the squares are lined up in a straight line as shown in the image given below
Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e they cannot be broken.)

Total perimeter for the above arrangement = AB + BC + CD +AD = 9/2 + 9/2 + 1/2+ 1/2 = 20/2 = 10m.

After such an arrangement, we will still have the greater perimeter as compared to fig.10.7(i). i,e., 10m > 6m

NCERT Solutions for Class 6 Maths Chapter 10 Exercise 10.1 Question 17

Avneet buys 9 square paving slabs, each with a side of 1 / 2 m. He lays them in the form of a square. (a) What is the perimeter of his arrangement [Fig 10.7(i)]? (b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [(Fig 10.7 (ii)]? (c) Which has greater perimeter? (d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)

Summary:

(a) The perimeter of Avneet's arrangement of squares is 6 m. (b) The perimeter of Shari's arrangement of squares is 10 m. (c) Shari's arrangement of the squares has a greater perimeter than that of Avneet. (d) The perimeter of Avneet's arrangement can be made greater that is 10 m if all the squares are lined up in a straight line.

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