SOLUTION: A regular hexagon has sides of length 8cm. With the aid of a diagram find the perpendicular distance between two opposite faces.

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Question 1132208: A regular hexagon has sides of length 8cm. With the aid of a diagram find the perpendicular distance between two opposite faces.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A regular hexagon has sides of length 8cm. With the aid of a diagram find the perpendicular distance between two opposite faces.
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r = 8 cm
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apothem = sqrt(8^2 - 4^2)
perpendicular distance between two opposite faces = 2*apothem

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Think of the regular hexagon as being composed of 6 equilateral triangles.

The distance between opposite edges (not faces) is twice the height of one of the equilateral triangles. Dividing each equilateral triangle into two 30-60-90 right triangles shows the height of each triangle to be (sqrt(3)/2) times the edge length.

And that makes the distance between opposite edges (sqrt(3)) times the edge length.