Answer:

90 sq. units

Step-by-step explanation:

Solving for the length of the larger and smaller rectangles:

Larger rectangle:

• L₁ = 2x + 2(3) = 2x + 6
• W₁ = x + 2(3) = x + 6

Smaller rectangle:

• L₂ = 2x
• W₂ = x

Area of the larger rectangle

= L₁W₁

= (2x + 6)(x + 6)

= 2x² + 12x + 6x + 36

= 2x² + 18x + 36

Area of the unshaded or smaller rectangle

= L₂W₂

= 2x(x)

= 2x²

Given that the area of the big rectangle is 6 times the area of the unshaded rectangle or the smaller rectangle, we get

2x² + 18x + 36 = 6(2x²)

2x² + 18x + 36 = 12x²

10x² - 18x - 36 = 0

5x² - 9x - 18 = 0

(x - 3)(5x + 6) = 0

x - 3 = 0

x₁ = 3

5x + 6 = 0

5x = -6

x₂ = -6/5

We want x to be positive, so x = 3.

Area of the shaded part

= (Area of the larger rectangle) - (Area of the smaller rectangle)

= L₁W₁ - L₂W₂

= (2x + 6)(x + 6) - 2x(x)

= 2x² + 18x + 36 - 2x²

= 18x + 36

Substituting x = 3, we get

= 18(3) + 36

= 54 + 36

= 90 sq. units