Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regula
r hexagon with a perimeter of 7.5 in. What is the length of the dotted line? Round to the nearest hundredth.
2 answers:
Answer: The length of the dotted line is 3.75 inches.
Please refer to the picture attached for the missing part of the question
Step-by-step explanation: From the information given we have a regular hexagon, that is a six-sided polygon (all sides equal) with the perimeter given as 7.5 inches. The perimeter is the distance all around the figure, hence to determine the length of one side,
Length = 7.5/6
Length = 1.25
Also, the interior angles of a hexagon can be derived with the formula;
Angles = 180 (n - 2)
Where n is the number of sides of the polygon
Interior Angles = 180 (6 - 2)
Interior Angles = 180 x 4
Interior Angles = 720
If the total of the interior angles equals 720, then each angle can be calculated as;
Each Angle = 720/6
Each Angle = 120
Please refer to attached picture tagged SOLUTION Diagram)
Taking triangle GED as shown in the picture, angle E and angle D measure 60 degrees each. This is because angle E in the entire hexagon ABCDEF measures 120 degrees. The line from point G in the center of the hexagon divides the angle into two equal halves. Same applies to all other five angles in the hexagon. Having angle E and D equal to 120 (that is 60 + 60) angle G would be equal to 180 - 120 {sum of angles in a triangle equals 180) which gives us 60. In effect we have an equilateral triangle, with all angles equal. This also means all sides are equal, hence if line ED equals 1.25, it simply means line GE and line GD equals 1.25 as well.
From this result we can now conclude that the line that runs across the hexagon from point F to point C is 1.25 plus 1.25 which equals 2.50.
The dotted line as indicated in the question runs across one side of the hexagon and all through another hexagon, hence the total length of the dotted line equals;
Dotted line = 1.25 + 2.50
Dotted line = 3.75
Therefore the length of the dotted line is 3.75 inches
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