P
1P
2P
3P
4P
4P
5 is a regular hexagon. A and B are movable points on P
1P
2 and P
2P
3 respectively.
ABCD is a square with C and D in the same side of AB as P4. ABC'D' is a square on the other side.
Find the total area of all points that can be on segment CD.
Find the total area of all points that can be on segment C'D'.
I must be misunderstanding the problem, because I find its solution to be trivial:
I say that CD is essentially a tracing of AB parallel to AB a distance
AB away (as it is with opposite sides of a square), on the 'p4' side. Saying CD is on the p4 side of AB is the same as saying it's _not_ on the p2 side of AB. All CDs drawn this way are 'legal' as per the constraints of the problem, even though some CDs extend partially or fully outside the hexagon (for the bigger squares). So the loci of CD points is identical in area to the loci of AB points. All possible ABs 'fill-in' triangle (p1,p2,p3), which has an area of (base x height) = sqrt(3) (1/2) = sqrt(3)/2, for a unit side regular hexagon.
With the same logic, I see no differences for the loci of C'D' points and get the same area.
So what am I missing , please?
unlikely solution
