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HELP..... IT'S URGENT

a regular hexagon has sides of 8cm. find the perpendicular distance between two opposite faces​

User Spurdow
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1 Answer

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Answer:

8√3 ≈ 13.86 cm

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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HELP..... IT'S URGENT a regular hexagon has sides of 8cm. find the perpendicular distance-example-1
User Maxim Paperno
by
8.8k points

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