Get the Maximum Area!

[yoshiki]

Please help me with this question:
A farmer has four straight pieces of fencing: 1, 2, 3, and 4 metres in length. What is the maximum area, in metres, that he can enclose by connecting the pieces? Assume the land is flat

Please help me with this question.

[18experience]

Get a piece of paper. ALWAYS draw the 4 side on the bottom. These will have to be drawn to scale.

Configuration 1:
Draw it so that the 1 side is not connected to the 4 side (1 is "parallel" to the 4 side, although it probably won't be perfectly parallel). Make sure it is a convex shape (i.e., if you had five points, made a pentagon, not a star). The convex shape should (I think) always give you the largest area. Figure out the area of that shape. To do this, just chop your shape into triangles and squares.

Now, switching the position of the 2 and 3 sides will result in the same area, so we don't need to do that.

Configuration 2:
Draw it so that the 2 side is not connected to the 4 side. Find the area.

Configuration 3:
Draw it so that the 3 side is not connected to the 4 side. Find the area.

Its not very elegant, but it should get you the correct answer.


EDIT: OK, I thought about this some more, and that would not work. Please disregard this algorithm. The correct algorithm will have something to do with finding the best angles at which to connect the sides, vectors I believe they are called.