The area of the shaded region found using the dimensions of the squares is 12·(2·x - 3)·(x - 1) square inches
The steps used to find the area of the shaded region is as follows;
The area of the shaded region is the difference between the area of the of the rectangle and the area of the unshaded region
The dimensions of the rectangle are;
Width = (5·x - 6) inches
Height = (5·x - 6) inches
There above dimensions indicates that the rectangle is a square
The dimensions of the unshaded square are;
Width = x
Height = x
The area of the larger square is; A is; (5·x - 6) × (5·x - 6) = 25·x² - 60·x + 36
Area of the smaller square is; x × x = x²
The difference in the areas is; ΔA = Area of the large square - Area of the small square
ΔA is; 25·x² - 60·x + 36 - x² = 24·x² - 60·x + 36
Using technology, we get; 24·x² - 60·x + 36 = 12·(2·x - 3)·(x - 1)
Area of the shaded region = 12·(2·x - 3)·(x - 1)