Problem Solving

A thin piece of wire \(40\) meters long is cut into two pieces. One piece is used to form a circle with a radius of \(r,\) and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of \(r?\)

A. \(\pi r^2\)

B. \(\pi r^2+10\)

C. \(\pi r^2+14\pi^2 r^2\)

D. \(\pi r^2+(40-2\pi r)^2\)

E. \(\pi r^2+(10-12\pi r)^2\)

Answer: E

Source: GMAT Prep