trangle wrote:A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius 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. πr^2
b. πr^2+10
c. πr^2+1/4π^2r^2
d. πr^2+(40-2πr)^2
e. πr^2+(10-1/2πr)^2

I assume the radius r is in meters.

Length of wire used to form the circle of radius r meters = Perimeter of the circle = 2Ï€r meters
Therefore length of wire used to form the square = Remaining portion of the wire = (40 - 2Ï€r) meters

Therefore length of each side of the square = (40 - 2Ï€r)/4 meters

Area of the circular region = πr² sq. meters
Area of the square region = [(40 - 2πr)/4]² sq. meters = [10 - (πr/2)]² sq. mete

Therefore total are = πr² + [10 - (πr/2)]² sq. meters

Please check the options.
Option E is dimensionally incorrect. May be there is a typo.