Question

Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in.
The length of the dotted line is
in. Express the answer to the nearest hundredth.

Answer 1

The correct answer is:

3.75 in.

The length of the dotted line is 3.75 in.

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Answer 2

Answer:

3.75 in

Step-by-step explanation:

Since this figure is regular (all of the sides are congruent), the length of each side would be the perimeter, 7.5, divided by the number of sides, 6:

7.5/6 = 1.25 in.

To find the length across one entire hexagon:

We can draw 6 small triangles from the center of the hexagon.  We will work with the triangle at the bottom.

The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360 (the amount of a complete rotation around the center point) divided by 6 is 60°.

This will be an isosceles triangle.  The top vertex of this triangle is in the center of the hexagon; this means the length of the segment connecting this vertex to the bottom two vertices of the triangle will be the same.  (Think of it as the radius of a circle, the same from the center to every outside point.)

The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°.  Since the triangle is isosceles, the base angles will be equal:

120/2 = 60

The bottom two angles will also be 60°.  This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.

This means across the dotted line we have 1.25+1.25+1.25 = 3.75.