Answer:
8√3 ≈ 13.86 cm
Step-by-step explanation:
You want the perpendicular distance between opposite sides of a regular hexagon of side length 8 cm.
Triangle
Opposite sides of a regular hexagon can be considered to be opposite sides of a rectangle. The diagonal of that rectangle divides it into two 30°-60°-90° triangles. The ratio of side lengths of such a triangle is ...
1 : √3 : 2
The short side of that triangle is one side of the hexagon, so is 8 cm. The distance of interest is the other leg of that right triangle, so is ...
8√3 cm = distance between opposite sides
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Additional comment
In case you don't remember the ratios of sides of a 30°-60°-90° triangle, you can figure the length of interest using the trig relation ...
Tan = Opposite/Adjacent
tan(60°) = (distance between sides)/(one side)
distance between sides = (8 cm)√3 ≈ 13.86 cm
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