find polygon with the largest perimeter
Find polygon with the largest perimeter
To find the polygon with the largest perimeter, we need to consider the properties of different polygons. The perimeter of a polygon is the sum of the lengths of all its sides. So, to maximize the perimeter, we need a polygon with the maximum number of sides and each side should be as long as possible.
In general, polygons with more sides tend to have a larger perimeter. Among regular polygons, the circle has an infinite number of sides and therefore has the largest perimeter for a given area. However, if we are considering only non-circular polygons, the regular polygons with the maximum number of sides will have the largest perimeter.
The regular polygons with the largest number of sides are:
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Polygon with 3 sides (Equilateral Triangle): An equilateral triangle is a regular polygon with all sides and angles equal. Since it has the smallest number of sides among regular polygons, it will have the smallest perimeter among regular polygons.
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Polygon with 4 sides (Square): A square is a regular polygon with all sides and angles equal. It has more sides than an equilateral triangle, so its perimeter will be larger than that of an equilateral triangle for the same area.
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Polygon with 5 sides (Regular Pentagon): A regular pentagon is a polygon with five equal sides and angles. It has more sides than a square, so its perimeter will be larger than that of a square for the same area.
Continuing this pattern, as the number of sides increases, the perimeter also increases. Therefore, the regular polygon with the largest number of sides will have the largest perimeter.
In conclusion, if we are considering only non-circular polygons, the regular polygon with the largest number of sides will have the largest perimeter.