geometry

You basically have two rectangles:
a. the bigger rectangle is the floor with a surface of m*n
b. the smaller rectangle is the rug. The are of this one is (are of floor) - (area not covered by the rug).
The are not covered by the rug will be 2*p*n + 2*(m - 2p)*p. This means that the surface of the rug will be mn - 2pn - 2pm + 4p^2 = (mn - 2pm) - (2pn - 4p^2) = m(n - 2p) - 2p(n - 2p) = (m - 2p)(n - 2p).

Another way of solving this is considering length of rug = x and width of rug = y. Then x = m - 2p (since you've got a strip of p length on the right and one on the left) and y = n - 2p (since you 've got a strip of p length on the top and one on the bottom). This makes area = (m - 2p)(n - 2p). This method is slightly faster.

My guess is E.

Answer is E

thankyou Danaj, excellent explanation