A square purple rug has a red square in the center. The side length of the red square is X inches. The width of the purple band that surrounds the Red Square is 10 inches. What is the area of the purple band?

The area of the orange square rug (including the yellow square) is 10*10=100 square inchesthe area of the orange square rug without the yellow square is 100 minus the area of the yellow squarethe area of the yellow square is x*x=x2therefore the area is (100-x2) square inches