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.

3 regular hexagons are connected at their sides. A dotted line is drawn through the middle of the 3 hexagons. The top image is a reflection of the bottom image. The dotted line is the length of one side and the distance from one point of the hexagon to the opposite point.

What is the length of the dotted line? Round to the nearest hundredth.

2.50 in.
3.75 in.
5.00 in.
6.25 in.

Answer 1

The answer is B. 3.75 in.

Good luck:)

Answer 2

The length of the dotted line in the hexagon is 3.75cm.

How to find the length across one entire hexagon?

We can draw 6 small triangles from the center of the hexagon. The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360.

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.

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