Certainly! Let's walk through the steps to understand the problem and arrive at the correct expression.
We need to find the expression that should be subtracted from the area of the rectangle in order to find the area of the parallelogram RSTU.
1. Understand the context:
- Parallelogram RSTU is inscribed within a rectangle.
- Each vertex of the parallelogram touches a side of the rectangle.
2. Area Relations:
- The area of the rectangle includes the area of the parallelogram plus the areas of the triangles formed around the parallelogram within the rectangle.
3. Triangle Areas:
- By drawing the parallelogram inside the rectangle, several smaller triangles are created outside the parallelogram but inside the rectangle.
- To find the area of the parallelogram, we need to subtract the area of these triangles from the area of the rectangle.
4. Expression:
- The expression representing the total reduction (subtraction) due to the triangles created around the parallelogram needs to be considered.
5. Correct Expression:
- The correct expression to determine the area of the parallelogram involves the geometric method where adding the lengths of the sides of the rectangle plays a significant role.
- From the provided choices, the expression [tex]\( 2(18 + 4) \)[/tex] fits the scenario most accurately.
Therefore, after evaluating the situation, the expression that can be subtracted from the area of the rectangle to find the area of parallelogram RSTU is:
[tex]\[
2(18 + 4)
\][/tex]
This leads to a numerical value of:
[tex]\[
2 \times (18 + 4) = 2 \times 22 = 44
\][/tex]
Hence, the correct choice is:
[tex]\[
2(18 + 4)
\][/tex]
