The image presents a composite rectangular painting divided into four regions. We are tasked with finding the total area of the painting. The dimensions of the smaller rectangles are labeled in terms of $x$. Let's analyze step by step:

1. The entire painting is a rectangle with:

   • Width = $x + 4$
   • Height = $x + 6 + x + 2 = 2x + 8$

2. Area of the entire rectangle: The formula for the area of a rectangle is $\text{Area} = \text{Width} \times \text{Height}$. Substituting: $\text{Area} = (x + 4)(2x + 8)$

3. Expand $(x + 4)(2x + 8)$: $\text{Area} = x(2x + 8) + 4(2x + 8)$ $\text{Area} = 2x^2 + 8x + 8x + 32$ $\text{Area} = 2x^2 + 16x + 32$

Thus, the area of the painting is: $\boxed{2x^2 + 16x + 32}$

Would you like a step-by-step explanation of the expansion or further assistance with similar problems?

5 Related Questions:

1. How do you calculate the perimeter of this painting?
2. What would the dimensions of the painting be if $x = 5$?
3. Can you divide this painting's area into smaller rectangular areas for each color?
4. What is the role of factoring in determining the dimensions from the area formula?
5. How do changes in $x$ affect the total area of the painting?

Tip:

Always simplify expressions step by step to avoid missing terms or making calculation errors!