A goat is tied by a 14 $m$ rope to a peg at one corner of a square field of side 30 $m$, and it grazes only inside the field. Find the area of the field it cannot reach, in $m^2$. Take π = 22/7.

Two fences meet at the corner, so the goat sweeps a quarter circle of radius 14 $m$: ¼ × $(22/7)\times 196=154m^2$. The field measures $30^2=900{\text{m}}^2$, so the part out of reach $=900-154=746{\text{m}}^2.(154{\text{m}}^2$ is the grazed part, the opposite of what is asked; allowing a whole circle instead of a quarter leaves $900-616=284{\text{m}}^2.$)