To solve this problem, let's follow a step-by-step method.
1. Identify the dimensions of the rectangle:
- The length of the rectangle is 18 units.
- The width of the rectangle is 4 units.
2. Calculate the area of the rectangle:
- The area of a rectangle is given by the formula [tex]\( \text{Length} \times \text{Width} \)[/tex].
- So, the area of this rectangle is [tex]\( 18 \times 4 = 72 \)[/tex] square units.
3. Understand the relationship between the rectangle and the parallelogram:
- The parallelogram RSTU is inscribed within the rectangle, meaning that vertices of the parallelogram touch the sides of the rectangle.
- Given this inscribed setup, two right triangles on either side of the parallelogram are included in the rectangle but are not part of the parallelogram.
4. Calculate the area to be subtracted (sum of the two triangles not part of the parallelogram):
- The area to be subtracted consists of two triangles that share a common base and height with the sides of the rectangle.
- The area of a triangle is calculated using the formula [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \)[/tex].
- Since the base and height match the sides of the rectangle, the expression for one triangle's area would be [tex]\( \frac{1}{2} \times 18 \times 4 \)[/tex].
- To get the sum for the two triangles, we need to double this value.
5. Formulate the appropriate expression for the subtraction:
- Summarizing the areas of the two triangles, we get: [tex]\( 2 \times \left( \frac{1}{2} \times 18 \times 4 \right) \)[/tex].
- Simplifying this gives us: [tex]\( 2 \times \left( \frac{1}{2} \times (18 + 4) \right) \)[/tex].
Since the question specifies that we need subtraction, this can further simplify as:
[tex]\[ 2(18 + 4) = 2 \times 22 = 44 \][/tex]
6. Choose the correct expression:
- The correct expression is [tex]\( 2(18 + 4) \)[/tex].
Therefore, to find the area of the parallelogram RSTU by subtracting from the area of the rectangle, we use the expression [tex]\( 2(18 + 4) \)[/tex].
