Surface area of a hexagonal prism is 613 mm^2. Find the dimensions (h is height, e is edge length).
asked Nov 5, 2017 in Geometry Answers by anonymous

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1 Answer

Surface area of hexagon = 613=6eh + 3e²√3. 3√3=5.196152 approx.

Therefore h=(613-3e²√3)/(6e).

There is no unique solution but since h is positive, e must be less than 10.86mm approx.

Here are some related values.

e (mm) h (mm)
0.5 203.90
1 101.30
1.5 66.81
2 49.35
2.5 38.70
3 31.46
3.5 26.16
4 22.08
4.5 18.81
5 16.10
5.5 13.81
6 11.83
6.5 10.09
7 8.53
7.5 7.13
8 5.84
8.5 4.66
9 3.56
9.5 2.53
10 1.56
10.5 0.64

When the height and edge are equal h=e=7.3994mm approx.

answered Mar 9 by Rod Top Rated User (546,020 points)

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