The shaded region's area is x² + 23x + 49.
Step-by-step explanation:
Step 1; To calculate the area of the shaded region, we subtract the area of the square which has side lengths of (x + 1) from the entire rectangle. So we determine the equations that denote the areas of the two shapes.
Step 2; Area of the square = side length × side length (x + 1)×(x + 1) = x² + x + x + 1 = x² + 2x + 1
Area of the bigger rectangle = length × breadth = (x + 10) × (2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50.
Step 3; The given shaded region's area = Area of the bigger rectangle - Area of the smaller square = 2x² - x² + 25x - 2x + 50 - 1 = x² + 23x + 49.
So the shaded region's area of x² + 23x + 49.
