A dog is tied to the corner of a house with a regular hexagonal base that measures 6 ft. on each side. If the rope is 12 ft. in length, what is the area in square feet of the region outside the house that the dog can reach?

1 Answer
Mar 7, 2017

Area of the region outside the house that the dog can reach is #339.29# square feet

Explanation:

As the dog is tied to a corner of a hexagon, with a rope of length of #12# feet, his movement is indicated in the following figure.

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As may be seen, he has freedom of movement in a circle of #12# feet radius but within a sector of #240^@# only. Then he reaches next corner, on either side and has a movement restricted to #6# feet in an arc of #60^@# only.

Hence the area of the region outside the house that the dog can reach is given by

#240/360xxpixx12^2+2xx60/360xxpixx6^2#

= #2/3xx144xxpi+2xx1/6xx6^2xxpi#

= #96pi+12pi#

= #108pi#

= #108xx3.1416#

= #339.29# square feet