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Tentukan bilangan segi tiga yang boleh dibina

The question involves a hexagon and asks for the number of triangles that can be formed inside it and the sum of the interior angles. Let's analyze the question step by step:

1. **Number of Triangles in a Hexagon**:
   - A regular hexagon can be divided into **6 equilateral triangles** by connecting the center of the hexagon to all its vertices.
   - Additionally, if forming triangles between vertices without including the center, you can form triangles by choosing 3 vertices from the 6 vertices of the hexagon. The total combinations are calculated as:
     \[
     \binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20
     \]
     This gives 20 possible triangles.

2. **Sum of Interior Angles of the Hexagon**:
   - The formula for the sum of interior angles of a polygon is:
     \[
     \text{Sum of interior angles} = (n - 2) \times 180^\circ
     \]
     Here, \( n = 6 \) (number of sides of the hexagon), so:
     \[
     (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
     \]

### Final Answer:
- **Number of Triangles**:
  - 6 equilateral triangles from the center.
  - 20 additional triangles from combinations of vertices.
  - Total: 26 triangles (if both methods are considered).

- **Sum of Interior Angles**: \( 720^\circ \).

Let me know if you need further clarification or calculations. Here are 5 related questions for deeper understanding:

1. How can the properties of a regular hexagon assist in forming equilateral triangles?
2. What is the formula for combinations, and how is it applied here?
3. How does the sum of interior angles of a polygon change with the number of sides?
4. Can this process be generalized to polygons other than a hexagon?
5. How can we calculate the area of the equilateral triangles formed within a regular hexagon?

**Tip**: To explore geometric relationships, drawing all possible diagonals helps visualize hidden patterns.

Tentukan bilangan segi tiga yang boleh dibina di dalam heksagon.

Learn how to calculate the number of triangles that can be formed inside a hexagon and the sum of its interior angles. Includes detailed explanations of geometry, polygon properties, and combinatorics. Perfect for Grades 7-9.

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