It seems like you're working with two polynomial terms, \(5x^3\) and \(4x^2\), and you'd like to find the area of a rectangle. To calculate the area of a rectangle, you multiply its length by its width.

If we assume the length is \(5x^3\) and the width is \(4x^2\), the area \(A\) of the rectangle is given by:

\[
A = \text{Length} \times \text{Width}
\]
\[
A = (5x^3) \times (4x^2)
\]

Now, multiplying the coefficients (5 and 4) and adding the exponents of \(x\):

\[
A = 20x^{3+2} = 20x^5
\]

So, the area of the rectangle is:

\[
A = 20x^5
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the area of the rectangle if \(x = 2\)?
2. How do you find the area of a rectangle with different polynomial sides?
3. What is the perimeter of this rectangle given the same side lengths?
4. How do you simplify polynomial multiplication in general?
5. Can the area ever be negative?

**Tip**: When multiplying powers with the same base, you add the exponents!

This problem explains how to find the area of a rectangle when the sides are given as polynomial expressions (5x^3 and 4x^2). Using algebraic techniques like polynomial multiplication and exponent rules, we derive the area as 20x^5. Suitable for students in Grades 9-11.

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