A square rug has an inner square in the center. The side length of inner square is x inches and the width of the outer region is 2 inches. What is the area of the outer part of the rug?

so Area of Outer part = 8x + 16 square inches

Step-by-step explanation:

2 squares.

inner square dimension is  x inches by x inches.

width of outer region= 2inches.

We want the area of the border around the inner square.

so

Area of border = B  =  Area of Large - Area of Inner

B = (x+4)^2  - x^2

B = x^2 + 8x + 16 -  x^2

B = 8x + 16  square inches

so Area of Outer part = 8x + 16 square inches