Question

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.
Width = x^2+2
Base = x-1
Height = x+1

Answer 1

To find the area of a parallelogram, we use the formula:

\[
\text{Area} = \text{Base} \times \text{Height}
\]

In this problem, the base and height of the park (which is in the shape of a parallelogram) are given as:

- Base = \( x - 1 \)
- Height = \( x + 1 \)

Now, we will substitute these expressions into the formula for area:

\[
\text{Area} = (x - 1)(x + 1)
\]

Next, we need to multiply these two binomials. We can use the difference of squares formula, which states that \( (a - b)(a + b) = a^2 - b^2 \).

Here, \( a = x \) and \( b = 1 \). Therefore, we have:

\[
(x - 1)(x + 1) = x^2 - 1^2 = x^2 - 1
\]

Thus, the area of the park, represented by the polynomial expression, is:

\[
\text{Area} = x^2 - 1 \quad \text{(square units)}
\]

This results in the final polynomial expression for the area of the park:

\[
\text{Area} = x^2 - 1
\]

So the answer is:

\[
x^2 - 1
\] square units.