To solve this problem, let’s break it down into smaller steps:
1. Drawing the Rectangle: Imagine you draw a rectangle around the parallelogram RSTU. The rectangle's sides are such that each vertex of the parallelogram touches one of the rectangle's sides.
2. Calculating the Area of the Rectangle:
- Let’s denote the length of the rectangle as [tex]\(18\)[/tex] and the width as [tex]\(4\)[/tex].
- Therefore, the area of the rectangle is calculated by multiplying its length and width:
[tex]\[
\text{Area of the rectangle} = \text{Length} \times \text{Width} = 18 \times 4 = 72
\][/tex]
3. Understanding the Geometry:
- Each side of the parallelogram forms four pairs of right triangles within the rectangle.
- These triangles are formed between the sides of the parallelogram and the sides of the rectangle.
4. Area to be Subtracted:
- To find the area of the parallelogram, we need to subtract the area of these triangles from the area of the rectangle.
- The triangles combined make up a certain area that’s part of the rectangle but not part of the parallelogram.
5. Expression for the Subtracted Area:
- Since each triangle is paired, the total area to be subtracted can be represented by the value [tex]\(2(18 + 4)\)[/tex].
- Here, we are essentially summing the dimensions of the rectangle and multiplying by 2 to account for the geometry involving the right triangles and the parallelogram.
Therefore, the correct expression to subtract from the area of the rectangle to determine the area of parallelogram RSTU is:
[tex]\[
2(18 + 4)
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{2(18+4)}
\][/tex]
