SOLUTION: A regular hexagon has sides of length 8cm Find the perpendicular distance between two opposites faces

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Question 1180055: A regular hexagon has sides of length 8cm
Find the perpendicular distance between two opposites faces
Answer by MathLover1(20849) About Me  (Show Source):
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The internal angles of a regular hexagon is 360%2F6+=+60 degrees

The diagonals connecting the two edges of opposite sides makes equilateral triangles with apex at the centre.

Hence the perpendicular distance would be twice that of the longer side of a 30/60/90 degree triangle with hypothenuse 8cm.

Using Pythagoras theorem
d+=+2%2Asqrt%288%5E2+-+4%5E2%29
d+=+2%2Asqrt%2864+-+16%29
d+=+2%2A+sqrt%2848%29
d+=+8sqrt%283%29
Hence this length would be 8sqrt%283%29cm exactly, or +13.9cm approximately