A piece of wire 5 inches long is to be cut into two pieces. One piece is x inches long and is to be
bent into the shape of a square. The other piece is to be bent into the shape of a circle. Find an
expression for the total area made up by the spare and the circle as a function of x.

Question

anonymous · Answer

Area of a square is $$s ^{2}$$  The bent piece of wire will have side lengths of x/4.  So the area of the square is $$(x/4)^{2}$$

The rest of the wire is 5" - x.  That will comprise the circumference of the circle. $$C = 2 \pi r$$  We can solve this for r and then use that to find the are of the circle.
$$r = (5-x)/2 \pi$$
Area of a circle is $$\pi r ^{2}$$
So you can substitute the r value into the equation and solve for that area as well.  
Enjoy.