Avneet buys 9 square paving slabs, each with a side of $ \frac{1}{2} \mathrm{~m} $. He lays them in the form of a square.

(a) What is the perimeter of his arrangement [Fig (i)]?
(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What isthe perimeter of her arrangement [(Fig (ii)]?
(c) Which has greater perimeter?
(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find away of doing this? (The paving slabs must meet along complete edges i.e. they cannotbe broken.)"

Given:

Avneet buys 9 square paving slabs, each with a side of \( \frac{1}{2} \mathrm{~m} \). He lays them in the form of a square.

To do:

We have to find:

(a) The perimeter of the arrangement in [Fig (i)].

(b) The perimeter of Shari's arrangement in [(Fig (ii)].

(c) Which among the two has greater perimeter.

(d) If there is a way of getting an even greater perimeter. (The paving slabs must meet along complete edges i.e. they cannot be broken.)

Solution:

(a) Length of the square formed $ = 3\times$ each side of the slab

$ = 3\times\frac{1}{2} $ 

$ = \frac{3}{2}$

We know that,

The perimeter of a square with side $a$ is $4a$.

Therefore,

Perimeter of the square $ = 4\times\frac{3}{2}$

$ =2\times3$

$=6\ m$

The perimeter of his arrangement is $6\ m$.

(b) We know that,

Perimeter is defined as the length of the outline of a shape.

To find the perimeter of a figure, just add the lengths of all the sides of the figure.

The perimeter of the arrangement made by Shari $ = 0.5+1+1+0.5+1+1+0.5+1+1+0.5+1+1$

$ =10\ m$

The perimeter of the arrangement made by Shari is $10\ m$.

(c) The arrangement made by Shari has greater perimeter than the square made by Avneet.

(d) There is no way of getting an even greater perimeter by paving the slabs in any other form.

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Updated on: 10-Oct-2022

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