Area of a circle? Geometry?

The square area consists of 4 equal sides each of which has a length of square_root(36) = 6 m.

So, the total length of the fence is 4x6 = 24 m.

The farmer reuses this fence to construct a circular area of circumference 2πR = 24, where R is the radius of the circle. The above gives R = 12/π.

So the are of this circle is πR^2 = 144/π = 45.86 sq.m. (almost).

Notice that with the same length of fence, the farmer now got a bigger 'farm'. Actually the circle is the geometry that can give you the biggest possible area.

Mind that the above solution can only be approximated (that's what I said "almost"). This is a computational (or numerical solution) and not a pure mathematical (analytical) one.

This problem referred as "Squaring the Circle" was first stated by ancient Greek mathematicians to be impossible to solve. Which still holds true to our present times.

You should have all of the formulas you need for this already.

The square plot has an area of 36 m^2, so how long is each side?

Now that you know how long each side is, what is the total perimeter? That's how much fence is available.

If a circular enclosure is made instead, the total amount of fence represents the circle's circumference. You know the circle's circumference; what's its radius?

From the radius, you should be able to find the area.