To find the area of the parallelogram RSTU by using the area of a rectangle around it, we can follow these steps:
1. Identify the dimensions of the rectangle:
Given that the vertices of the parallelogram are on the sides of the rectangle, let's assume the dimensions of the rectangle are given by the lengths 18 (length) and 4 (width).
2. Calculate the area of the rectangle:
For a rectangle, the area is given by:
[tex]\[
\text{Area of rectangle} = \text{length} \times \text{width} = 18 \times 4 = 72
\][/tex]
3. Understand the method chosen by Juan:
Juan draws a rectangle around the parallelogram and aims to subtract smaller areas to find the area of parallelogram RSTU. The area of parallelogram RSTU can be found by subtracting certain parts (likely triangles or other sections) from the area of the rectangle.
4. Substitute each given option and identify the valid expression:
- Option 1: [tex]\( 2(18 + 4) \)[/tex]
[tex]\[
2(18 + 4) = 2 \times 22 = 44
\][/tex]
This doesn't fit the concept of subtracting from 72 to get the parallelogram area.
- Option 2: [tex]\( \frac{1}{2}(18 + 4) \)[/tex]
[tex]\[
\frac{1}{2}(18 + 4) = \frac{1}{2} \times 22 = 11
\][/tex]
Same as above, but leads to less valuable reduction here.
- Option 3: [tex]\( 18 + 4 \)[/tex]
[tex]\[
18 + 4 = 22
\][/tex]
It's also a wrong fit for our goal.
- Option 4: [tex]\( 18 - 4 \)[/tex]
[tex]\[
18 - 4 = 14
\][/tex]
The valuable fit into subtraction sub-object areas.
5. Find correct matches using the explanation for parallelogram area deductions:
Conclusively, option:
- Matched [tex]\(44\)[/tex],
- Leading to suit [tex]\(44\)[/tex].
دادن
