You own a goat and a meadow. The meadow is in the shape of an equilateral triangle each side of which is 100 meters long. The goat is tied to a post at one corner of the meadow. How long should you make the tether in order to give the goat access to exactly half the meadow?

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Draw a hexagon whose sides are 100 meters long. Now draw a circle, with the same center, whose radius r is the desired length of the tether:
The difference in area between the hexagon and the circle is 6 times half the area of the meadow.
The area of the circle is πr^{2}.
The area of an equilateral triangle with side length a is .
The area of a hexagon with side length a is .
For a = 100 the area of the hexagon is . If we want a circle half that size, then and
(From Ian Stewart’s Cabinet of Mathematical Curiosities, 2009.)
