A goat is tied by a 14 $m$ rope to a corner peg of a square shed of side 7 $m$ standing in an open field. The goat grazes only outside the shed, and the rope bends round the walls when it is pulled tight. Find the total grazing area in $m^2$. Take π = 22/7.

At the peg the wall blocks 90°, so the goat sweeps 270° at radius 14 $m:(3/4)\times (22/7)\times 196=(3/4)\times 616=462m^2$. Round each adjacent corner the rope left over is 14 − 7 = 7 $m$ and it sweeps a further 90°: $(1/4)\times (22/7)\times 49=38.5m^2$, and there are two such corners, adding $77{\text{m}}^2$. (The 7 $m$ left just reaches the far corner, so nothing is counted twice.) Total $=462+77=539{\text{m}}^2$.