Michael is finding the area of parallelogram ABCD. To do this, he follows the steps in the table.
| Step 1 | Draw a rectangle around parallelogram ABCD. |
|---|---|
| Step 2 | Find the area of the rectangle. |
| Step 3 | Find the area of the four right triangles created in the corners of the rectangle. |
| Step 4 | Subtract the area of the right triangles from the area of the rectangle. |
To solve the problem using these steps, what are the dimensions of the rectangle he should draw?
A. 2 units by 4 units
B. 3 units by 2 units
C. 4 units by 4 units
Answer (2)
The problem cannot be solved because the dimensions of the parallelogram are not provided. Without knowing the dimensions of the parallelogram ABCD, it is impossible to determine the dimensions of the rectangle that should be drawn around it.
Explanation
Analyze the problem and available data. The problem describes a method to find the area of a parallelogram by enclosing it in a rectangle and subtracting the areas of the surrounding right triangles. However, the problem does not provide any information about the dimensions or angles of the parallelogram ABCD. Without this information, it's impossible to determine the dimensions of the rectangle that Michael should draw. The problem seems to be missing crucial information, making it unsolvable with the given data.
Explain the impossibility of determining the dimensions. Since we don't have any information about the parallelogram's dimensions or angles, we cannot determine the dimensions of the surrounding rectangle. Therefore, none of the provided options (2 units by 4 units, 3 units by 2 units, or 4 units by 4 units) can be definitively chosen as the correct answer.
Conclude the solution. Due to the lack of information about the parallelogram ABCD, we cannot determine the dimensions of the rectangle that Michael should draw around it.
Examples
In architecture, when calculating the area of a plot of land that is shaped like a parallelogram, architects often enclose the parallelogram within a rectangle. They then calculate the area of the rectangle and subtract the areas of the triangles formed outside the parallelogram but inside the rectangle. This method simplifies the area calculation, especially when dealing with irregularly shaped plots.
The dimensions of the rectangle that Michael should draw around parallelogram ABCD cannot be determined, as the dimensions of the parallelogram are not provided. Without this information, it is impossible to select an option from the choices given. Therefore, none of the available options can be definitively chosen as the correct answer.
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