Drawing a polygon, especially a regular polygon, involves a systematic approach often utilizing geometric principles. Based on the method described, a key step in drawing a regular polygon involves calculating an angle based on the number of sides.
Understanding Regular Polygon Drawing
A regular polygon has all sides of equal length and all interior angles of equal measure. While there are multiple methods to draw polygons (like using a compass and protractor for regular ones, or simply connecting vertices for irregular ones), the reference points to a method focused on turning angles.
The Key Calculation from the Reference
A fundamental step in drawing a regular polygon, as highlighted in the provided reference, is to determine the exterior angle you need to turn at each vertex after drawing a side.
The reference specifically states: "you have to calculate 360 IDE by the number of side of your polygon."
This calculation, 360° / number of sides, gives you the measure of the exterior angle. When drawing, this is the angle you turn outside the polygon to draw the next side. For example, to draw a polygon with 6 sides (a hexagon), you would calculate 360° / 6 = 60°. This means you draw a side, turn 60°, draw the next side, turn 60°, and so on.
Step-by-Step Guide to Drawing a Regular Polygon (Exterior Angle Method)
Utilizing the principle from the reference, here's a simplified guide to drawing a regular polygon:
- Draw the First Side: Begin by drawing a straight line segment of your desired length. This will be the first side of your polygon.
- Calculate the Turn Angle: Determine the number of sides (n) your polygon will have. Use the calculation from the reference: Angle = 360° / n. This is the angle you will turn after drawing each side.
- Turn and Draw the Next Side: Place your drawing tool (like a ruler) at the end of the first line segment. Measure and turn by the calculated angle (the exterior angle) from the direction of the first line. Then, draw the second side, making sure it is the same length as the first.
- Repeat: Continue this process – turn by the calculated angle and draw a side of the same length – until you have drawn all n sides and the shape is closed, connecting back to your starting point.
Example: Drawing a Regular Pentagon (5 sides)
Let's apply the method to draw a 5-sided regular polygon (a pentagon):
- Number of Sides: n = 5
- Calculate Angle: Angle = 360° / 5 = 72°
- Draw:
- Draw side 1.
- Turn 72°. Draw side 2.
- Turn 72°. Draw side 3.
- Turn 72°. Draw side 4.
- Turn 72°. Draw side 5. (This side should meet the beginning of side 1).
Following this method ensures all sides are equal and all exterior turns are equal, resulting in a regular polygon.
Tips for Accuracy
- Use a ruler to ensure all sides are the same length.
- Use a protractor to measure the turn angle accurately at each vertex.
- Start with a clear workspace and sharp drawing tools.
By calculating the turn angle based on the number of sides (360° divided by the number of sides, as mentioned in the reference), you can effectively draw any regular polygon.
