Answer the Questions(?) in the details page below, please! Thanks!

You have a regular hexagonal fenced area in your backyard. Rover, your dog, is tied with a 12-meter chain at one of the vertices of the regular hexagon. The perimeter of the fence is 78 meters. Your veterinarian recommends that Rover have at least 150 square meters of roaming room. Does Rover have enough roaming room? How much roaming room does Rover have? You must answer both questions. Write an explanation of how you got your answer.

1 Answer
Mar 19, 2018

Yes, about #150.8" m"^2#

Explanation:

Since the perimeter of the hexagon is 78 m, each side is 13 m long. Rover can roam within a distance of #R=12" m"# from the vertex he is tied to (the one on the extreme right in the picture below) - i.e. within the sector of the circle shown.

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The angle contained in the sector is the internal angle of a regular hexagon #theta =(2pi)/3#.

Thus, the area that Rover can roam over is

#1/2 theta R^2 = 1/2 times (2 pi)/3 times 12^2" m"^2 ~~ 150.8" m"^2#