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It is a regular polygon
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- Because it is a regular polygon, a square is the quadrilateral of least perimeter enclosing a given area.
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What is a regular polygon?
Are regular polygons equiangular?
What are regular polygons with equal sides and angles?
What are the properties of a regular polygon?
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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.
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.
- 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.
A polygon is a plane shape (two-dimensional) with straight sides. Examples include triangles, quadrilaterals, pentagons, hexagons and so on. Regular. Here we look at Regular Polygons only. Properties. So what can we know about regular polygons? First of all, we can work out angles. All the Exterior Angles of a polygon add up to 360°, 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\[A=\frac{3\sqrt{3}}{2}s^2\]
Sep 5, 2021 · 7.1: Regular Polygons. A regular polygon is a polygon in which all sides are equal and all angles are equal, Examples of a regular polygon are the equilateral triangle (3 sides), the square (4 sides), the regular pentagon (5 sides), and the regular hexagon (6 sides).
A square is a regular polygon with four equal sides and equal angles that each measure 90°. For a quick refresher, a regular polygon is a two-dimensional enclosed figure made by joining three or more straight lines. Now, let’s identify some real world examples of squares! Squares in the real world.
