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

1 answer

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.