A goat is tied by a 7 $m$ rope to a corner peg of a shed whose base is an equilateral triangle of side 5 $m$. The goat grazes outside the shed only, and the rope bends round the corners of the walls. Find the total grazing area in $m^2$. Take π = 3.14.

The wall blocks the 60° corner, so the goat sweeps 360 − 60 = 300° at radius 7 $m:(300/360)\times 3.14\times 49=128.22m^2$. Round each of the other two corners the rope left over is 7 − 5 = 2 $m$ and it sweeps 180 − 60 = 120°: $(120/360)\times 3.14\times 4=4.19m^2$ each, $8.37{\text{m}}^2$ for the two (2 + 2 < 5, so these never overlap behind the far wall). Total $=128.22+8.37=136.59{\text{m}}^2$. (153.86 is the full circle; 128.22 forgets the corners; 140.78 lets the rope sweep 180° at each corner.)