Question

Avneet buys 9 square paving slabs, each with a side of `1/2` m. He lays them in the form of a square.

1. What is the perimeter of his arrangement [Fig (i)]?
2. 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)]?
3. Which has greater perimeter?
4. 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.)

Answer 1

1. Side of square = 3 × side
   = `3 xx 1/2`
   = `3/2`m
   Perimeter of Square = `4 xx 3/2`
   = 2 × 3
   = 6 m
2. Perimeter = 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1
   = 10 m
3. The arrangement in the form of a cross has a greater perimeter.
4. Perimeters greater than 10 m cannot be determined.