Okay, set up a coordinate system so that your square has vertices at (0, 0), (1, 0), (0, 1), and (1, 1). The smallest area triangle that will fit around that is the right triangle having (0, 0) as the vertex of the right angle and hypotenuse passing through (1, 1). If we call the point at which the hypotenuse touches the x-axis (X, 0) and the point at which it touches the y axis (0, Y), then the area of the triangle is and, using "similar triangles", or .

So the problem becomes "minimize subject to the constraint .