To find the area of the rectangle, we need to multiply the height and the width together. The area $A$ of the rectangle is given by:

$A = \text{height} \times \text{width}$

Given:

• Height = $7a^2$
• Width = $a^4 + 5a^2 + 4$

The area is:

$A = 7a^2 \times (a^4 + 5a^2 + 4)$

Now, to calculate this, distribute $7a^2$ to each term in the width expression:

$A = 7a^2 \times a^4 + 7a^2 \times 5a^2 + 7a^2 \times 4$

Simplifying each term:

$A = 7a^6 + 35a^4 + 28a^2$

Thus, the area of the rectangle is:

$A = 7a^6 + 35a^4 + 28a^2$

This is the area expressed as a polynomial in standard form.

Would you like more details on the solution or have any questions?

Here are some related questions:

1. How do we simplify polynomials involving multiple terms?
2. What are the properties of a polynomial in standard form?
3. How can we interpret the area of a rectangle in terms of algebraic expressions?
4. What happens if we change the height or width of the rectangle?
5. How can the distributive property be used in polynomial multiplication?

Tip: Always ensure you correctly distribute terms when multiplying polynomials to avoid missing any components!