The area of the orange band is 28x + 196 square inches.
The Breakdown
To calculate the area of the orange band surrounding the blue square, we need to subtract the area of the blue square from the area of the larger orange square.
The side length of the blue square is given as x inches. Therefore, the area of the blue square is x² square inches.
The width of the orange band surrounding the blue square is 7 inches. This means that the side length of the larger orange square is (x + 2 × 7) inches, as there are two orange bands on each side of the blue square.
The area of the larger orange square is (x + 2 × 7)² square inches.
To find the area of the orange band, we subtract the area of the blue square from the area of the larger orange square:
Area of orange band = Area of larger orange square - Area of blue square
= (x + 2 × 7)² - x²
= (x + 14)² - x²
= x² + 28x + 196 - x²
= 28x + 196 square inches
Therefore, the area of the orange band is 28x + 196 square inches.