https://file.aiquickdraw.com/mathbot/file/17302113224811x83897n.jpg

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.

Tentukan luas persegi panjang KLMN berikut.

Learn how to calculate the area of rectangle KLMN given the diagonal length of 7 cm and an angle of 60 degrees. This solution involves using trigonometric ratios to find side lengths, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation