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The text in the image is in Indonesian and translates to:

"An equilateral triangle and a regular hexagon have the same perimeter. If the area of the triangle is 4, what is the area of the hexagon?"

Let's break it down to solve it.

### Given:
- The perimeter of an equilateral triangle is equal to the perimeter of a regular hexagon.
- The area of the equilateral triangle is 4 square units.

### Let the side of the equilateral triangle be \( a \), and the side of the hexagon be \( b \).

1. **Perimeter Condition**:  
   - The perimeter of the equilateral triangle = \( 3a \)  
   - The perimeter of the hexagon = \( 6b \)  
   Since both perimeters are equal:
   \[
   3a = 6b \quad \Rightarrow \quad a = 2b
   \]

2. **Area of the Equilateral Triangle**:  
   The area \( A \) of an equilateral triangle with side \( a \) is given by:
   \[
   A = \frac{\sqrt{3}}{4} a^2
   \]
   Since the area is given as 4:
   \[
   \frac{\sqrt{3}}{4} a^2 = 4 \quad \Rightarrow \quad a^2 = \frac{16}{\sqrt{3}} \quad \Rightarrow \quad a = \sqrt{\frac{16}{\sqrt{3}}}
   \]

3. **Side of the Hexagon**:  
   Since \( a = 2b \), we can find \( b \) by dividing \( a \) by 2:
   \[
   b = \frac{a}{2}
   \]

4. **Area of the Regular Hexagon**:  
   The area \( A \) of a regular hexagon with side length \( b \) is given by:
   \[
   A = \frac{3\sqrt{3}}{2} b^2
   \]

Let's calculate the final values for the area of the hexagon next.The side length of the equilateral triangle is approximately \( a = 3.04 \) units, and the side length of the regular hexagon is \( b = 1.52 \) units. 

The area of the regular hexagon is approximately \( 6 \) square units.

Would you like more details or explanations on any part of this problem?

Here are 5 related questions to explore:
1. How does the perimeter of a shape relate to its area?
2. What are other methods to calculate the area of regular polygons?
3. How does the number of sides of a polygon affect its area for a given perimeter?
4. Can this problem be generalized for any regular polygon with equal perimeters?
5. How does the formula for the area of an equilateral triangle derive from basic geometry?

**Tip:** Remember that for regular polygons with the same perimeter, increasing the number of sides will generally increase the enclosed area!

Segitiga sama sisi dan segi enam beraturan memiliki keliling yang sama. Jika luas segitiga adalah 4, berapa luas segi enam?

Learn how to calculate the area of a regular hexagon when its perimeter is equal to that of an equilateral triangle, given that the triangle’s area is 4. This solution involves key geometry concepts and formulas suitable for students in Grades 8-10.

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