To find the area of rectangle $KLMN$, let's analyze the information given in the problem:

1. $\angle KLM = 60^\circ$.
2. The length of diagonal $KL = 7 \, \text{cm}$.

Step-by-Step Solution:

1. Determine the Lengths of $KN$ and $LM$:

   • Since $KLMN$ is a rectangle, the diagonals $KL$ and $MN$ are equal and form right triangles with sides $KN$ and $LM$.
   • In $\triangle KLM$, we can use trigonometric ratios to find $KN$ and $LM$.

2. Using Trigonometry:

   • For $\angle KLM = 60^\circ$:
     • $KN = KL \cdot \cos(60^\circ) = 7 \times \frac{1}{2} = 3.5 \, \text{cm}$.
     • $LM = KL \cdot \sin(60^\circ) = 7 \times \frac{\sqrt{3}}{2} \approx 6.06 \, \text{cm}$.

3. Calculate the Area:

   • The area of the rectangle $KLMN$ is given by $\text{Area} = KN \times LM$.
   • Substituting the values: $\text{Area} = 3.5 \times 6.06 \approx 21.21 \, \text{cm}^2$

Final Answer:

The area of rectangle $KLMN$ is approximately $21.21 \, \text{cm}^2$.

Would you like further details on any of these steps, or do you have any other questions?

Here are 5 related questions to further explore this topic:

1. How would the area change if $\angle KLM$ was different?
2. What if only the length of $KN$ was given? How would you find the area?
3. How would you find the perimeter of rectangle $KLMN$?
4. How can the Pythagorean theorem be used to verify the diagonal's length?
5. What is the importance of trigonometric ratios in solving rectangle area problems?

Tip: When solving rectangle problems with diagonals, always consider using trigonometric functions if an angle is given.