Asked by hudson
Use the image to answer the question.
A parallelogram has its length labeled x-squared plus 2 and its width labeled x plus 1. It has a dashed line for its height labeled x minus 1.
A park is in the shape of a parallelogram with dimensions shown. Determine the polynomial expression that represents the area of the park, in square units.
(1 point)
$$
A parallelogram has its length labeled x-squared plus 2 and its width labeled x plus 1. It has a dashed line for its height labeled x minus 1.
A park is in the shape of a parallelogram with dimensions shown. Determine the polynomial expression that represents the area of the park, in square units.
(1 point)
$$
Answers
Answered by
GPT-4o mini
To find the area of a parallelogram, you can use the formula:
\[
\text{Area} = \text{Base} \times \text{Height}
\]
From the information provided:
- The base (length) is \( x^2 + 2 \)
- The height is \( x - 1 \)
Now we can substitute these expressions into the area formula:
\[
\text{Area} = (x^2 + 2)(x - 1)
\]
Next, we need to expand this expression:
\[
\text{Area} = x^2 \cdot (x - 1) + 2 \cdot (x - 1)
\]
Calculating each part:
1. \( x^2 \cdot (x - 1) = x^3 - x^2 \)
2. \( 2 \cdot (x - 1) = 2x - 2 \)
Now combine these results:
\[
\text{Area} = x^3 - x^2 + 2x - 2
\]
Putting it all together, the polynomial expression that represents the area of the park is:
\[
\boxed{x^3 - x^2 + 2x - 2}
\]
\[
\text{Area} = \text{Base} \times \text{Height}
\]
From the information provided:
- The base (length) is \( x^2 + 2 \)
- The height is \( x - 1 \)
Now we can substitute these expressions into the area formula:
\[
\text{Area} = (x^2 + 2)(x - 1)
\]
Next, we need to expand this expression:
\[
\text{Area} = x^2 \cdot (x - 1) + 2 \cdot (x - 1)
\]
Calculating each part:
1. \( x^2 \cdot (x - 1) = x^3 - x^2 \)
2. \( 2 \cdot (x - 1) = 2x - 2 \)
Now combine these results:
\[
\text{Area} = x^3 - x^2 + 2x - 2
\]
Putting it all together, the polynomial expression that represents the area of the park is:
\[
\boxed{x^3 - x^2 + 2x - 2}
\]
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