For this, we need to find the area of the larger rectangle (The room) and subtract from that the area of the smaller, shaded rectangle (The rug).
A=LW (L=Length, W=Width, A=Area)
The larger rectangle first:
A=(15)(10)
A=150 feet squared
Now the Rug:
A=(12)(7)
A=84 feet squared
Now to find the area that is NOT covered by the rug, we subtract:
150-84
= 66 feet squared will NOT be covered by the rug.
Hope this Helps!
-Sinnamin