12.5π/4 ? The locus of point M is 1/4 arc with the radius of 1/2 centered on ABCD respectively (that is, it can be combined into a circle) and a short section in the middle of each of the four sides of a square. Let the side length be x and the length of each segment be x- 1.

l = 2π×( 1/2)+4×(x- 1)= 4x-4+π？ S=x？ -π×( 1/2)? =x？ -π/4?

L-S=4x-4+π-x？ +π/4 =-(x-2)？ +5π/4 ? The maximum value is 5π/4.

13.y=-x？ + 1(x >0)

Y'=-3x Let P(x 1, y 1), then the tangent through p is y=-3x 1? (x-x 1)+y 1

s=(2x 1？ + 1)? /6x 1？ =(2x 1？ +1/2x1+1/2x1)/6, so the minimum value is