How do you investigate the areas of regular polygons with a fixed perimeter of 12 units
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To investigate the areas of regular polygons with a fixed perimeter of 12 units, you can follow these steps:
1. Understand the concept: A regular polygon is a shape with equal sides and equal angles. For polygons with a fixed perimeter, their sides will still be equal but the number of sides may vary.
2. Determine the number of sides: Since the perimeter is fixed at 12 units, you need to figure out how many sides the regular polygon has. To do this, divide the perimeter (12) by the length of one side.
3. Calculate the length of one side: Divide the perimeter (12) by the number of sides. This will give you the length of one side.
4. Calculate the apothem (radius): The apothem is the distance from the center of the regular polygon to the midpoint of one of its sides. For regular polygons, the apothem can be calculated using the formula: apothem = side length / (2 * tan(180°/n)), where n is the number of sides.
5. Calculate the area: The area of a regular polygon can be calculated using the formula: area = (perimeter * apothem) / 2.
By following these steps, you can investigate the areas of regular polygons with a fixed perimeter of 12 units. Note that as the number of sides of the regular polygon increases, its shape will approach that of a circle, and its area will approach that of a circle as well (given the same perimeter).