Answer:
square inches.
Step-by-step explanation:
Given:
A square green rug has a blue square in the center.
The side length of the blue square is x inches as shown in the figure:
The width of the green band that surrounds the blue square is 6 inches.
Question asked:
What is the area of the green band ?
Solution:
<u>Side length of blue square = </u>
<u />
First of all we will calculate area of blue square.
As we know:


Thus, area of blue square =
Now, we will calculate area of square green rug:
Side length of green rug = Side length of blue square + width which surrounds the blue square
Side length of green rug = 
Thus, area of square green rug =
<em><u>Now, we will find area of the green band ( shaded region with green color as shown in the figure)</u></em>
Area of the green band = Area of square green rug - Area of blue square
![=(x+6)^{2} -x^{2} \\=(x+6+x)(x+6-x)\ [a^{2} -b^{2} =(a+b)(a-b)]](https://tex.z-dn.net/?f=%3D%28x%2B6%29%5E%7B2%7D%20-x%5E%7B2%7D%20%5C%5C%3D%28x%2B6%2Bx%29%28x%2B6-x%29%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%5Ba%5E%7B2%7D%20-b%5E%7B2%7D%20%3D%28a%2Bb%29%28a-b%29%5D)


Therefore, the area of the green band is
square inches.