Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
An area model for a rectangle that has a height of x plus five and a width of x plus six. The rectangle is broken into four rectangles to isolate each term in the height and the width. The top left rectangle has a height of x and a width of x. The top right rectangle has a height of x and width of six. The bottom left rectangle has a height of five and a width of x. The bottom right rectangle has a height of five and a width of six.


To find the area of the entire rectangle, we calculate the area of each of the four smaller rectangles and sum them up. The dimensions of the four smaller rectangles are:

1. **Top left rectangle**: Height = \(x\), Width = \(x\), Area = \(x \cdot x = x^2\)
2. **Top right rectangle**: Height = \(x\), Width = \(6\), Area = \(x \cdot 6 = 6x\)
3. **Bottom left rectangle**: Height = \(5\), Width = \(x\), Area = \(5 \cdot x = 5x\)
4. **Bottom right rectangle**: Height = \(5\), Width = \(6\), Area = \(5 \cdot 6 = 30\)

### Total Area
Adding these together, we have:
\[
\text{Total Area} = x^2 + 6x + 5x + 30
\]

### Combine Like Terms
\[
\text{Total Area} = x^2 + (6x + 5x) + 30 = x^2 + 11x + 30
\]

Thus, the area of the entire rectangle is:
\[
\boxed{x^2 + 11x + 30}
\]

Let me know if you want a breakdown of each step or have further questions!  

Here are 5 related questions to explore:

1. How would the area change if the height and width are increased by a constant value?
2. How do you factorize the polynomial \(x^2 + 11x + 30\)?
3. Can you explain the role of the distributive property in calculating the total area?
4. How would the result differ if one dimension is negative?
5. How can you graph the polynomial \(x^2 + 11x + 30\) and interpret its properties?

**Tip**: When working with polynomials, always simplify by combining like terms for a clearer standard form.

Express the area of the entire rectangle. An area model for a rectangle has a height of x plus five and a width of x plus six. The rectangle is broken into four smaller rectangles: Top left (x by x), Top right (x by 6), Bottom left (5 by x), and Bottom right (5 by 6).

Explore how to calculate the total area of a rectangle using polynomials. This problem demonstrates the distributive property and the combination of like terms, breaking the problem into four smaller rectangles for clarity. Perfect for students in Grades 7-9 learning algebra and polynomial expressions.

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