[tex]\text{Answer : Area is 6x}^2\text{ + 8x OR 2x(3x + 4)}[/tex]
The figure given is a rectangle
The larger rectangle is the outer rectangle while the inner rectangle is the smallest rectangle.
The area of a rectangle is given as
Area = Length x width
Length of the outer rectangle = 3x + 2
The width of the outer rectangle = 4x
The length of the inner rectangle = 2x
The width of the inner rectangle = 3x
The area of the shaded region = Area of the larger rectangle - area of the smaller rectangle
For the larger rectangle
Area = length x width
Area = (3x + 2) x 4x
Open the parenthesis
Area = 4x * 3x + 4x * 2
[tex]\begin{gathered} \text{Area = 12x}^2\text{ + 8x} \\ \text{For smaller rectangle} \\ \text{Area = length x width} \\ \text{Area = 2x }\cdot\text{ 3x} \\ \text{Area = 6x}^2 \\ \text{The area of the shaded region = area of the larger rectangle - area of the smaller rectangle} \\ \text{Area of the shaded portion = 12x}^2+8x-(6x^2\text{)} \\ \text{Area of the shaded region = 12x}^2+8x-6x^2 \\ \text{Collect the like terms} \\ \text{Area = 12x}^2-6x^2\text{ + 8x} \\ \text{Area = 6x}^2\text{ + 8x OR 2x(3x + 4)} \end{gathered}[/tex]
