Convex hexagon ABCDEF is equiangular but has no two sides the same length. Its sides in some order are 1, 2, 3, 4, 5 and 6 units long. If AB=1 and CD>BC, what are the lengths of BC, CD, DE, EF and FA?
Another convex hexagon is also equiangular and has sided measuring 1, X, 3, 4, 5, and 6 units long in that order going clockwise. What is the measure of X?
In an equiangular hexagon there are 3 pairs of parallel sides.
Given a pair of parallel sides, the consecutive pairs on either side must have the same sum. This results in the following:
AB + BC = DE + EF
BC + CD = EF + FA
CD + DE = FA + AB
To solve part 2 the first equation becomes
1+x=4+5 so x=8
To solve part 1 it seemed reasonable to make opposite sides of similar length. The order of the sides that work are
1, 4, 5, 2, 3, 6
another hexagon which doesn't satisfy CD>BC is
1, 5, 3, 4, 2, 6
Posted by Jer
on 2004-10-15 16:30:33