What is the solution to Dido's problem?

[pilpel]

Given a fixed perimeter, what is the geometric shape (non-self-intersecting closed curve) that would maximize the enclosed area? MathWorld (I'm not allowed to link) and a few other sites insist that the answer is a semi-circle, but simple math with perimeter=100 m would show that a circle would have area 2500/$\pi$$\approx$795.8 m$^{2}$ whereas a semicircle wold have area $\approx$594.2 m$^{2}$.

What am I missing?

 

[micromass]

Dido's problem demands that one side of the enclosure is a straight line of fixed length. A circle would not qualifiy, since it has no straight sides.

If you allow all closed curves, then the circle would be optimal.