Let the lengths of the two portions of wire be denoted by and .
Let the circle be constructed from the portion whose length is .
If the circumference of the circle is , then the radius can be found by rearranging the formula for the circumference of a circle.
Let the square be constructed from the portion whose length is . The side length of the square will therefore be .
Now find the area of each shape.
The total area to be minimized is therefore the sum of these two expressions.
Now differentiate with respect to .
Now set the derivative equal to 0 and solve for .
Hence, the length of the circle portion is .
The length of the square portion is
Hence, the length of the square portion is .