Problem Solving

a thin piece of wire 40 meter long is cut into 2 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?

answer is pie r^2 + (10-1/2pie r^2)

please show me how to even begin solving this problem, or what you do in solving a problem like this.

yvonne12 wrote:a thin piece of wire 40 meter long is cut into 2 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?

answer is pie r^2 + (10-1/2pie r^2)

please show me how to even begin solving this problem, or what you do in solving a problem like this.

The piece that forms the circle is of length 2*pi*r. So remaining is
40 - 2*pi*r

If perimeter of square is 40 - 2*pi*r, each side is 1/4th of that which is
10 - pi*r/2

So, total area = pi*r^2 + (10 - pi*r/2)^2

Say the length of first piece of wire is "t". This t = 2*pie*r (circumference of the circle)
Now the remainder of the wire after the circle is formed = 40 - t or in other words 40 - 2*pie*r (substituting for t)
Perimeter of square = 40 - 2*pie*r
Side of square = (40-2*pie*r)/4
Area of square = [(40-2*pie*r)/4]^2
= (10-r*pie/2)^2

Hence area of circle plus square = (10-r*pie/2)^2 + (pie*r)^2

Cybermusings

You couldnt have explained it any better. I understood the thought process. Thanks alot!