Radius and circle

pi*r^2 for circular
for square:
40 - 2*pi*r = perimeter of square (note that 2*pi*r = circumference of the circular)
((perimeter of square)/4)^2 = area of square
=> answer is the sum of these two (E)

r - radius of sq
length of wire left after circle cut over = 40-2pi*r

So, from left wire , we made a sq. SO perimeter of sq with side a

4a = 40 -2pi *r
a = (10- (pi*r/2))
sq this u ll find area of sq and area of circle u already know

this one is discussed in "3 Problems from the GMAT Prep Program"

Thanks for you explanations, but Im still not clear on this.

Can someone try to make it a little easier to understand?
Is there a link to another thread with more explanation that someone can share please?

Its simple. You need to know some formulae here:

Perimeter of a Circle (given radius r) is: 2*pi*r
Area of a circle is: pi*r^2

Perimeter of a square is: 4*length of side
Area of a square is: side^2

Based on the inputs from the question, we know that 'r' is the radius of the circle. So, the perimeter of the circle (length of wire used) is: 2*pi*r

So, the remaining wire is: (40-2*pi*r) that will be used for making a square. The side of the square (40-2*pi*r)/4 (since a square has 4 sides). So, the area of the square will be ((40-2*pi*r)/4)^2. This can be further reduced to (10-pi*r/2)^2

Adding both the areas will give you the answer: pi*r^2 + (10-pi*r/2)^2