If the circumference of a circle increases by 20%, how much is the area increased by?
Ummmmm...... He just did.
If a length change is made (in this case a circle which is 1-D) then a corresponding change to an area is indicated.
So if we have a circle with circumference C and we increase it by 20% then the new circumference is now 1.2C. So the corresponding area (originally A) would increase by a factor of $\displaystyle 1.2^2$, ie. the new area is $\displaystyle 1.2^2A$.
-Dan
To harpazo: You did not answer my reply: "For the circumference to increase what must change?"
Well, the circumference is $\pi D=\pi\cdot 2r$ where $D$ is diameter & $r$ is radius.
The old area is $\pi r^2$ and the new increased area is $\pi(1.2r)^2$.
Remember what that I told you before the percent of change is $\dfrac{New-Old}{Old}$. SEE HERE.