We are tasked with calculating the area of a rectangle based on the given dimensions. The area $A$ of a rectangle is calculated using the formula:

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

From the image:

• Width = $\frac{7}{c+6}$
• Length = $\frac{5(c+6)}{11c}$

Step 1: Multiply the dimensions

$A = \left( \frac{7}{c+6} \right) \times \left( \frac{5(c+6)}{11c} \right)$

Step 2: Simplify the expression

We can cancel out the $(c+6)$ terms from both the numerator and the denominator:

$A = \frac{7 \times 5}{11c}$

$A = \frac{35}{11c}$

Final Answer:

The area of the rectangle is:

$A = \frac{35}{11c}$

This is the area in its simplest form.

Would you like further details on how I simplified the expression?

Here are five related questions to further your understanding:

1. What would happen to the area if $c$ were doubled?
2. How does the area change if the width becomes $\frac{8}{c+6}$?
3. What is the relationship between the dimensions and the area of any rectangle?
4. Can the area formula be used for other shapes, like triangles or circles?
5. How would the area formula change if this was a square instead of a rectangle?

Tip: Always cancel common terms when multiplying fractions—it simplifies calculations!