Avneet buys 9 square paving slabs, each with a side of 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 is the 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 a way of doing this? (The paving slabs must meet along complete edges, i.e., they cannot be broken)

(a) From the given figure, the side of one slab is m

Therefore, the side of square = (3 × ) m = m

Now,
We know that the perimeter of a square = 4 × Side

= 4 × = 6 m

(b) We know that,

Perimeter = Sum of all sides

Therefore Perimeter = 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1

= 10 m

(c) The arrangement which is in the shape of cross has a greater perimeter (i.e. 10 m)

(d) If we put all 9 slabs in a line then, the perimeter will be 10 m, as shown below.

Thus, from the given arrangements, arrangements with perimeters greater than 10 m cannot be determined.