A path 1 $m$ wide runs inside a square garden of side 25 $m$, all along the boundary. Find the area of the path in $m^2$.

The path eats 1 m from each of the two opposite sides, so the grass left is a square of side 25 − 2 = 23 m. Path = $25^2-23^2=625-529=96{\text{m}}^2$. (Multiplying the perimeter by the width, $4\times 25\times 1=100{\text{m}}^2$, counts each of the four corner squares twice; $104{\text{m}}^2$ is the answer for a path of the same width laid OUTSIDE the garden, $27^2-625$; $24{\text{m}}^2$ is one strip only.)