ASAP PLS> 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.

Each polygon is a regular hexagon with a perimeter of 7.5 in.
That means that each side of a hexagon is: 7.5 : 6 = 1.25 in.
The length indicated by the dotted lines:
1.25 * 3 = 3.75 in.
Answer:
The length is 3.75 inches.

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wifilethbridge wifilethbridge · Answer 2 · 2019-04-17T07:29:44+02:00

Answer:

3.75 inches

Step-by-step explanation:

We are given a regular hexagon.

This means all six sides of each polygon are equal .

Since perimeter of each polygon= 7.5 in.

So, perimeter of regular hexagon = [tex]6 \times Side[/tex]

So, [tex]7.5 =6 \times Side[/tex]

[tex]\frac{7.5}{6} = Side[/tex]

[tex]1.25 = Side[/tex]

Since AB is the side of the regular polygon .

So, length of AB is 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.

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:

[tex]\frac{120}{60}[/tex]

The bottom two angles will also be 60°. This makes the equilateral triangle whose all 3 sides will be 1.25.

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

Hence the length of dotted line is 3.75 inches.