Draw and illustrate a regular decagon of side length 6 cm with 144° interior angles

To draw and illustrate a regular decagon (10-sided polygon) with a side length of 6 cm and interior angles of 144°, follow these steps:

### Materials Needed:
- Compass
- Ruler
- Protractor
- Pencil
- Paper

### Steps to Draw a Regular Decagon:

1. **Draw a Circle:**
   - Use a compass to draw a circle with an appropriate radius to accommodate the side length of 6 cm for the decagon. The radius \( r \) can be calculated using the formula \( r = \frac{a}{2 \sin(\frac{\pi}{n})} \), where \( a \) is the side length and \( n \) is the number of sides.
   - For a decagon (n = 10) with a side length of 6 cm:
     \[
     r = \frac{6}{2 \sin(\frac{\pi}{10})} \approx 9.404 \, \text{cm}
     \]
   - Set the compass to approximately 9.404 cm and draw the circle.

2. **Mark the Center:**
   - Mark the center of the circle as point \( O \).

3. **Divide the Circle:**
   - Use a protractor to divide the circle into 10 equal parts. Each central angle will be \( \frac{360°}{10} = 36° \).

4. **Mark the Points:**
   - From the center \( O \), mark points on the circumference of the circle at every 36°. Label these points as \( A, B, C, \ldots, J \).

5. **Draw the Sides:**
   - Using a ruler, connect the points consecutively \( A \) to \( B \), \( B \) to \( C \), and so on, until you connect \( J \) back to \( A \).

### Illustration:
Below is an illustration of the decagon with the described steps:

1. Draw a circle with radius approximately 9.404 cm.
2. Mark the center \( O \).
3. Divide the circle into 10 equal segments (each 36°).
4. Connect the points on the circumference to form the decagon.

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Learn how to draw a regular decagon with a side length of 6 cm and interior angles of 144° using compass, ruler, and protractor. This problem covers key geometric concepts including circle geometry and properties of regular polygons. Suitable for students in Grades 9-12.

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