To find the area of parallelogram RSTU, Juan considers drawing a rectangle around it, where each vertex of the parallelogram touches a side of the rectangle. We can use this approach to determine which expression may be subtracted from the area of the rectangle to get the area of the parallelogram.
Let's break down the process step-by-step:
1. Draw the Rectangle:
- Juan starts by enclosing the parallelogram RSTU within a rectangle.
2. Calculate the Rectangle's Area:
- Assume the dimensions (length and width) of this rectangle are known, but for the purpose of this problem, let's consider the overall structure first.
3. Identify the Triangle Areas:
- When the parallelogram is inscribed within the rectangle, four right triangles are formed outside the parallelogram but inside the rectangle (one at each corner).
4. Areas of the Triangles:
- Each triangle formed outside the parallelogram is identical in dimension due to the symmetry. Therefore, the total area of these four triangles needs to be considered.
5. Subtracting Triangle Areas:
- To find the area of the parallelogram, subtract the combined area of these triangles from the area of the rectangle. Given that these are four identical triangles, let’s compute as per the provided values:
Understanding from the correct context:
- Juan correctly identifies that the area of these triangles, due to the two identical sets on each axis of the rectangular structure, equate to the expression 2(18 + 4).
6. Conclusion:
- When identifying the area of the parallelogram within the rectangle, the combined areas of the triangles, represented by 2(18 + 4), are to be subtracted from the total area of the rectangle.
Answer:
The correct expression to be subtracted from the area of the rectangle to find the area of parallelogram RSTU is:
[tex]\[ 2(18+4) \][/tex]
Thus, the correct choice is:
[tex]\[
2(18 + 4)
\][/tex]
