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If all the sides and interior angles of the polygons are equal, they are known as regular polygons. The examples of regular polygons are square, rhombus, equilateral triangle, etc. In regular polygons, not only the sides are congruent but angles are too.
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- What Is A polygon?
- Parts of A Polygon
- What Are Regular polygons?
- Properties of Regular Polygons
- Perimeter of A Regular Polygon
- Sum of Interior Angles of A Regular Polygon
- Measure of Each Interior Angle of A Regular Polygon
- Measure of Each Exterior Angle of A Regular Polygon
- Number of Diagonals of A Regular Polygon
- Number of Triangles of A Regular Polygon
A two-dimensional enclosed figure made by joining three or more straight lines is known as a polygon. They are also known as “flat figures”. Example: A square is a polygon with made by joining 4 straight lines of equal length.
A polygon has three parts: 1. Sides: A line segment that joins two vertices is known as a side. 2. Vertices: The point at which two sides meet is known as a vertex. 3. Angles: interior and exterior. An interior angle is the angle formed within the enclosed surface of the polygon by joining the sides.
If all the polygon sides and interior angles are equal, then they are known as regular polygons. The examples of regular polygons are square, equilateral triangle, etc. In regular polygons, not only are the sides congruent but so are the angles. That means they are equiangular.
The properties of regular polygons are listed below: 1. All its sides are equal. 2. All its interior angles are equal. 3. The sum of its exterior angles is 360°.
A regular polygon has all the sides equal. And the perimeter of a polygonis the sum of all the sides. So, a regular polygon with n sides has the perimeter = n times of a side measure. For example, if the side of a regular polygon is 6 cm and the number of sides are 5, perimeter = 5 ✕ 6 = 30 cm
Let there be a n sided regular polygon. Since, the sides of a regular polygon are equal, the sum of interior angles of a regular polygon = (n − 2) × 180° For example, the sides of a regular polygon are 6. So, the sum of interior angles of a 6 sided polygon = (n − 2) × 180° = (6 − 2) × 180° = 720°
Since a regular polygon is equiangular, the angles of n sided polygon will be of equal measure. A n sided polygon has each interior angle = Sumofinterioranglesn=(n−2)×180∘n For example, let’s take a regular polygon that has 8 sides. So, each interior angle = (8−2)×180∘8=135∘
There are n equal angles in a regular polygon and the sum of an exterior angles of a polygon is 360∘. So, the measure of each exterior angle of a regular polygon = 360∘n.
The number of diagonals in a polygon with n sides = n(n−3)2as each vertex connects to (n – 3) vertices. And in order to avoid double counting, we divide it by two. For example, if the number of sides of a regular regular are 4, then the number of diagonals = 4×12=2.
If the sides of a regular polygon are n, then the number of triangles formed by joining the diagonalsfrom one corner of a polygon = n – 2 For example, if the number of sides are 4, then the number of triangles formed will be (4 – 2) = 2.
Is Square a Regular Polygon? Yes, a square is a regular polygon because a regular polygon is a polygon in which all the sides are of equal length and all the angles are of equal measure. Since a square fulfills this property, it is considered to be a regular polygon.
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew.
We can learn a lot about regular polygons by breaking them into triangles like this: Notice that: the "base" of the triangle is one side of the polygon. the "height" of the triangle is the "Apothem" of the polygon. Now, the area of a triangle is half of the base times height, so:
It can be useful to know the formulas for some common regular polygons, especially triangles, squares, and hexagons. Areas of Regular Polygons. Equilateral triangle\[A=\frac{\sqrt{3}}{4}s^2\] Square\[A=s^2\] Regular pentagon\[A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}~s^2\] Regular hexagon\[A=\frac{3\sqrt{3}}{2}s^2\]
In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle.
