### Brain Teasers

# Grazing Cow

A cow is tied in a rectangular field, 20m by 10 m.

The cow is tied to the middle of one of the 20m long fences by a rope 25m long. There is a gap the cow can squeeze through in the middle of the other 20m long fence (assume a point).

How much land can the cow graze on?

The cow is tied to the middle of one of the 20m long fences by a rope 25m long. There is a gap the cow can squeeze through in the middle of the other 20m long fence (assume a point).

How much land can the cow graze on?

### Answer

He can get to the whole area of the field, + the area of a semi circle outside the field, and 2 areas of quarter circles where the rope extends around the sides of the fences.20*10 + (pi*15^2)/2 + 2* (pi*5^2)/4

200+pi*112.5 + pi*12.5

200 + pi * 125

Approx 593 square metres.

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