The village playground is shaped as a square of side 40 metres. A path of width $s$ metres is created around the playground for people to walk. Find an expression for the area of the path in terms of $s$.

$$\text{Outer square side}=40+2s\text{ metres (path on each side).}$$

Area of path = (outer area) - (playground area)

$$= (40 + 2s)^2 - 40^2$$

$$= (1600 + 160s + 4s^2) - 1600$$

$$= 4s^2 + 160s$$

$$= 4s(s + 40) \text{ sq. m}$$