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 square and the circle as a function of x.

Answer 1

x square and (5-x) circle

side of square = x/4
area of square = x^2/16

radius of circle = (5-x)/(2 pi)
area of circle = pi r^2 = pi(5-x)^2/(4 pi^2)

total area = x^2/16 + (5-x)^2/(4 pi)