A High School Math Question dealing with coordinate geometry This to me has never been seen before:

Square $ABCD$ with side length $5$. Name any point $20$ units from from point $D$ , $E$. From every random point inside the square $F$ rotate $E$ about $F$ $120$ degree counterclockwise. Compute Area  of the region formed by all of the image points of the rotation

I tried to draw a pic according to the description in the problem:

Can anyone explain what the problem is asking and give a comprehensible answer?
PS: This is not a question of my own. I did get this from my teacher. So I think there shouldn't be any problem solving this problem.
 A: Let's position the square conveniently.  Let $A=(-5,0)^T, B=(-5,5)^T, C=(0,5)^T, D=(0,0)^T$.  It is not clear whether $E$ ranges over the whole circle centered at the origin with radius $20$ or is some point on that circle.  I will take $E=(20,0)^T$.  It should be clear how to generalize the question.  We are asked to let $F$ range throughout the square, so let $F=(x,y)$.  The we evaluate $\vec{FE}$, rotate it $120^\circ$ around $F$ and find the area of the locus as $F$ varies.  $FE=(20-x,-y)^T$ and $E'=\begin {pmatrix}x\\y \end {pmatrix}+\begin {pmatrix} -\frac 12&-\frac {\sqrt 3}2\\\frac{\sqrt 3}2&-\frac 12 \end {pmatrix}\begin {pmatrix}20-x\\-y \end {pmatrix}=\begin {pmatrix}-10+\frac 32x+\frac {\sqrt 3}2y\\10\sqrt 3-\frac {\sqrt 3}2x+\frac 32y \end {pmatrix}$  
Now we can see that the choice of a particular $E$ does not matter to the size of the locus.  Changing the location will change the constants $-10, 10 \sqrt 3$, but not the size of the region created.  Let $E'(D)$ be where the rotation sends $E$ when $F=(0,0)^T$, then we get a square with corners $$E'(D)\\
E'(D)+(-\frac{15}2,\frac {5\sqrt 3}2)^T
\\E'(D)+(-\frac{15}2+\frac {5\sqrt3}2,\frac {5\sqrt 3}2\frac 52)^T\\
E'(D)+(\frac {5\sqrt3}2,\frac {15}2)^T$$
, side $5 \sqrt 3 \approx 8.66$and area $75$
A figure is below.  The square doesn't look quite like one because the scales don't match.  $E'(A)$ is the position $E$ is moved to when $F$ is at $A$.

