https://r2.erweima.ai/mathbot/image/1725591665808kt3k0g33.jpg

The image shows a rectangular figure where you are asked to calculate the area. The dimensions given are:

- **Base**: \( 2x + 8 \)
- **Height**: \( x^2 + 6 \)

The formula for the area \( A \) of a rectangle is:

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

Substituting the values provided:

\[
A = (2x + 8) \times (x^2 + 6)
\]

Let me expand this expression for the area.

\[
A = (2x + 8)(x^2 + 6)
\]
\[
A = 2x(x^2 + 6) + 8(x^2 + 6)
\]
\[
A = 2x^3 + 12x + 8x^2 + 48
\]

Thus, the expanded expression for the area is:

\[
A = 2x^3 + 8x^2 + 12x + 48
\]

Would you like more details on this, or do you have any questions?

Here are 5 related questions:
1. How do you find the perimeter of this rectangle?
2. What would happen to the area if the base increased by a factor of 2?
3. How would you solve for the area if a specific value for \(x\) was given?
4. Can you calculate the derivative of the area function with respect to \(x\)?
5. What are the critical points of the area function \(A(x)\)?

**Tip**: When multiplying polynomials, always distribute each term carefully to avoid errors.

Learn how to calculate the area of a rectangle with algebraic expressions for both the base and height. The problem involves expanding polynomials and applying the distributive property, suitable for students in Grades 8-10.

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