To solve this problem, we need to write an expression for the area of the shaded section of the rectangle and then expand the brackets.

Step 1: Dimensions of the shaded section

1. The length of the shaded section is given as $c + 8 - 4$, because the total length is $c + 8$, and we subtract the unshaded part (4 units). $\text{Length of shaded section} = c + 4$

2. The width of the shaded section is 3 (as given in the diagram).

Step 2: Area of the shaded section

The area of a rectangle is given by: $\text{Area} = \text{length} \times \text{width}$ Substituting the values: $\text{Area} = (c + 4) \times 3$

Step 3: Expand the brackets

Expanding the expression: $(c + 4) \times 3 = 3c + 12$

Final Expression:

The area of the shaded section is: $\boxed{3c + 12}$

Let me know if you have any questions or need further clarifications!

Relative Questions:

1. How would the expression change if the dimensions of the unshaded rectangle were modified?
2. Can this problem be solved differently using subtraction of areas? If so, how?
3. What are the implications if $c$ is negative or zero in this problem?
4. How does this formula help in solving real-world geometry problems?
5. Could you derive the total area of the larger rectangle from this shaded area expression?

Tip:

Always double-check your work when subtracting or adding dimensions in geometric problems to ensure accuracy!