Answer: The area of a square is given by the formula A = s², where s is the length of a side of the square.
The area of the inner square is therefore A_inner = x².
The width of the outer region is 4 inches, so the length of each side of the outer square is x + 8 inches (since the outer square consists of the inner square and two regions of width 4 inches each).
Therefore, the area of the outer square is:
A_outer = (x + 8)²
Expanding the square, we get:
A_outer = x² + 16x + 64
The area of the outer part of the rug is the difference between the area of the outer square and the area of the inner square:
A = A_outer - A_inner
= (x² + 16x + 64) - x²
= 16x + 64
Therefore, the area of the outer part of the rug is 16x + 64 square inches.
Explanation: