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What is the formula for finding the area of a regular polygon?
What is the formula for finding the area of a regular polygon?
The formula for finding the area of a regular polygon is (1/2) * apothem * perimeter, where the apothem is the distance from the center of the polygon to a side, and the perimeter is the total distance around the polygon.
How can the area of an irregular polygon be calculated?
How can the area of an irregular polygon be calculated?
The area of an irregular polygon can be calculated by dividing it into smaller, regular polygons, finding the area of each smaller polygon, and then summing up the areas of all the smaller polygons.
What is the relationship between the number of sides of a polygon and its area?
What is the relationship between the number of sides of a polygon and its area?
The relationship between the number of sides of a polygon and its area is that as the number of sides increases, the area of the polygon approaches the area of a circle with the same perimeter.
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Study Notes
Area of Regular Polygons
- The formula for finding the area of a regular polygon is:
A = (n × s²) / (4 × tan(180/n)), whereAis the area,nis the number of sides, andsis the side length.
Area of Irregular Polygons
- The area of an irregular polygon can be calculated by dividing the polygon into triangles and finding the area of each triangle, then adding them up.
Relationship between Number of Sides and Area
- The area of a polygon increases as the number of sides increases, but the relationship is not directly proportional.
- As the number of sides of a polygon increases, the polygon begins to resemble a circle, and its area approaches that of a circle with the same perimeter.
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