To find the area of a parallelogram, you can use the formula:
\[ \text{Area} = \text{base} \times \text{height} \]
In this context, you'll need to identify the base and the height of the parallelogram. Usually, the base is one of the sides of the parallelogram, and the height is the perpendicular distance from the opposite side to the base.
Let’s denote the base of the parallelogram as \( b \) and the height as \( h \). If you have these dimensions given in terms of polynomial expressions, you can substitute those values into the area formula.
For instance, if the base \( b \) is represented by the polynomial expression \( x + 3 \) and the height \( h \) is expressed as \( 2x - 5 \), then the area \( A \) of the parallelogram can be calculated as follows:
\[ A = b \times h = (x + 3)(2x - 5) \]
To compute this product, you can use the distributive property (also known as the FOIL method for binomials):
\[ A = x(2x) + x(-5) + 3(2x) + 3(-5) \] \[ A = 2x^2 - 5x + 6x - 15 \] \[ A = 2x^2 + x - 15 \]
This will give you the polynomial expression for the area of the parallelogram.
If you provide specific dimensions or polynomials for the base and height, I can help you perform the multiplication and find the specific area representation.
1 answer