A polygon is a geometric shape with at least three sides. It can be irregular or regular and can have a finite or infinite number of sides. There are also spherical polygons. In this article, we’ll learn about regular and irregular polygons.
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Regular and irregular polygons
Use a polygons worksheet to help your child understand regular and irregular polygons. You can download it free and print it as often as you like. These worksheets can be used as a whole class activity or as homework. These materials will help children to reinforce what they have learned and identify gaps in their knowledge.
Regular polygons have equal sides and angles, while irregular polygons do not. For example, an ABC triangle has three sides that are not the same length. It also has three angles that are not equal in length. This is what makes a pentagon irregular. If all five sides are not equal, it is an irregular polygon.
The difference between regular and irregular polygons lies in their shape. Regular polygons are symmetrical shapes with equal sides. In contrast, irregular polygons have equal lengths on opposite sides, so they aren’t squares.
Regular and irregular polygons with a finite number of sides
There are two types of polygons: regular and irregular. Regular polygons have equal lengths and angles on all sides. In an irregular polygon, one or more sides have unequal angles. For example, the triangle ABCD does not have equal lengths on all sides. The interior angles are not equal to each other.
An irregular polygon is closed and does not have equal sides or angles. Its perimeter is calculated by adding the lengths of each of its sides. The perimeter of an irregular polygon is 23 units. These polygons differ from their regular counterparts in several ways.
Regular polygons are those with a finite number of sides. Triangles have three sides, while quadrilaterals have four sides. However, some polygons have more than four sides.
Regular and irregular polygons with a finite number of sides
Depending on their sides and angles, polygons are categorized as regular or irregular. Regular polygons are closed figures with an equal number of sides, while irregular polygons have unequal lengths and angles. For example, a circle is not a polygon because its sides are not all of the equal length. In addition, a circle cannot be inscribed into another circle, which makes it an irregular polygon.
Regular polygons have the same number of sides, which makes them easier to construct, whereas irregular polygons do not. Regular polygons are equiangular and symmetric around a common center. There are numerous specialized formulas for the area of regular polygons, including the apothem.
Area: The area of a regular polygon is the amount of space contained within the polygon. There are several formulas for calculating the area, but the formula used depends on the kind of polygon. For example, the area of a trigon is equal to the area of its base and height. The area is measured in units of m2, cm2, or ft2.
Spherical polygons
Spherical polygons are spherical surfaces of genus zero with a boundary component formed by geodesic arcs. These surfaces do not always correspond to a standard sphere but have a trivial monodromy. Their developing maps are well-defined up to rotation of the SO(3). They also have a Riemannian metric of constant curvature.
The angles of a spherical polygon are always greater than those of a Euclidean polygon with the same number of sides. For example, a spherical polygon with n sides always has an angle sum greater than 180 degrees.
Spherical polygons can be drawn in a wide variety of patterns. The most common shape is the n-gon. It has three straight sides, a convex center, and two convex corners. A regular n-gon with a 180-degree corner angle looks like a hemisphere with evenly spaced dots. It fits in nicely with a regular tessellation.
