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. (Details Below)
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.
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.
1 Answer
Explanation:
This is a regular hexagon, so all sides are of equal length.
The perimeter of the hexagon is 78 metres, and it has 6 sides.
Each side is:
The sum of the interior angles of a regular polygon is given by:
Where
Sum of angles:
Each angle:
The length of chain is 12 metres.
From diagram:
Since
The chain describes an arc:
The area that Rover has to roam is the area of the sector:
We can find this area by using:
Area of a sector is:
Where
Convert
Our radius is
Area of sector:
This is approximately:
This is greater than the recommended area of
