A polygon is a plane figure characterised by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). A bounded planar area, a bounding circuit, or both together are sometimes called polygons in Euclidean geometry.
Some important terms and information about Polygon:
Sides - segments of polygonal circles
vertex - the point where two sides of a polygon meets
body - interior of polygon
A "gon" refers to a side of a polygon. A quadrilateral is a quadrilateral.
A polygon is a two-dimensional figure. The aposem (sometimes abbreviated as apo) of a regular polygon is the line segment from the center to the midpoint of one of the sides.
Interior angle: The angle formed by the vertices of a polygon within the area enclosed by the polygon.
Center point of a regular polygon: The point inside the polygon where all the vertices of the polygon are equidistant.
Congruent Polygons: Polygons with all congruent sides
Exterior angle: The angle formed by the vertices of the polygon outside the area enclosed by the polygon.
Calculating side lengths, diagonals, and angles of regular polygons, bisectors, perimeters, and areas are part of the survey and geometry curriculum.
Common polygon names (by number of sides) and some of their properties:
Monogon - Not commonly recognized as a polygon, but the term is sometimes used in some fields such as graph theory.
2. Digon - is not commonly recognized as a polygon in the Euclidean plane, but may exist as a spherical polygon.
3. Triangle (or Trine) - The simplest polygon that can exist in the Euclidean plane. You can align planes. Number of sides = 3.
4. Rectangle (or Rectangle) - The simplest polygon can intersect itself. The simplest polygon that can be concave. The simplest polygons cannot cycle. You can align planes.
5. Pentagon - The simplest polygon can exist as a regular star. The star pentagram is known as the pentagram or pentagram.
6. Hexagon - planes can be tiled.
7. Heptagon (or heptagon) - The simplest polygon is such that a compass and ruler cannot create a regular shape. However, it can be constructed using the noisis structure.
Polygons can be classified according to their convexity type
• Convexity means that a line drawn through the polygon (not touching its sides or corners) hits its boundary exactly twice. Therefore, no interior angle exceeds 180°. On the other hand, line segments with endpoints on the boundary only pass through points inside between the endpoints.
• Concave: Straight instead of convex. At least one interior angle should exceeds 180°.
• Simple: The boundary of the polygon does not intersect itself. All convex polygons are simple.
• Star polygons - Star polygons are regularly intersecting polygons. A polygon cannot be both a star and a star shape. The difference between this and the next is something to keep in mind when trying to find the area of a regular polygon.
• Star: From at least one point, the entire interior is displayed without intersecting edges. Polygons must be simple and can be either convex or concave. All convex polygons are stars.
• Non Convex: Finds lines that touch the boundary more than once. A line segment is between two boundary points outside the polygon.
• Simple: The boundary of the polygon does not intersect itself. All convex polygons are simple.
• Concave: Straight instead of convex. At least one interior angle should exceeds 180°.
• Self-intersecting: The boundary of the polygon is self-intersecting. The term complex is sometimes used as opposed to simple, but this can confuse the notion of complex polygons that reside in a complex Hilbert plane and have two complex dimensions. .
According to the equality and symmetry aspect
• Equal Angles: means that all angles have equal angles.
• Equilateral: “ Equi “ stands for equal and “ lateral “ stands for sides This means that all sides are of equal length.
• Regular: Equilateral and equiangular shapes.
• Circular: All four corners lie on a single circle known as the circumscribed circle. Another way of defining regularity is that a polygon is regular if it is both equilateral and equilateral, or if it is both periodic and equilateral. A regular polygon is a non-convex regular polygon.
• Coordination or Edge Transitivity: All sides share the same symmetry orbital. Also, polygons are tangential and tangential.
• Tangent: This means that all sides of the circle are tangent. Equiangular or Corner Transition: All corners are on the same symmetrical trajectory. Polygons are also periodic and equiangular.
How did you find the area of a regular polygon?
The area of a regular polygon is represented by the area enclosed by the sides/boundaries of the polygon. Therefore, we can say that to find the area of a regular polygon, we need to calculate the area it occupies.
Difference between perimeter and area of a regular polygon
Perimeter and area are often confused. However, their only similarity is that the area and perimeter do not depend on the interior angles of the polygon. Rather, they depend on the length of the sides. First, to clear up the confusion between these two measurable identities, we need to understand the fundamental differences.
Definition - It is defined as the total length of a polygon's boundary, obtained by adding the lengths of all its sides.
Formula - Perimeter of polygon = length of side 1 + length of side 2 + … + length of side N (for N-sided polygons)
Units - meters, centimeters, inches, feet, etc.
Definition - It is defined as the area of space enclosed by any polygon.
Formula - The area of a polygon is whether the polygon is regular or irregular.
Units - (meters)2, (centimeters)2, (inches)2, (feet)2,
Some formulas for known regular polygons are given below.
• Area of triangle = (1/2) * height * base
You can also use Heron's formula to find the area of a triangle if you know the side lengths.
Area = √s(s-a)(s-b)(s-c)s(s a)(s−b)(s−c), where s = perimeter/2 = (a + b + c)/2, a, b, c are the side lengths.
• Area of rectangle = (length) x (width)
• Area of Parallelogram = (height) x ( base)
• Area of trapezoid = (1/2) x (total length of parallel sides or base) *!height
• Area of rhombus = (1/2)x (product of both the diagonals).
How can you find the area of a regular polygon if you know the number of sides?
The area of a regular polygon = (number of sides × length of sides × aposem)/2, where the length of the aposem is given as l/(2tan(180/n)). where l is the side length and n is the number of side of a regular polygon.
In terms of the perimeter of a regular polygon, the area of a regular polygon = (perimeter x length)/2, where perimeter = number of sides x length of side It is.
Example: Find the area of a 5-sided regular polygon with a side length of 10 cm
As we understood in the discussion above, all we need to solve this problem is the side length. The applicable formula is – 1/4×√5(5+2√5)×(side)2
So 1/4*√5(5+2√5)*(10)2= 172.05 square centimeters.
Example: Find the area of a regular polygon with 6 cm sides and 10 cm height
Since it is a triangle here, the triangle formula for finding area is used.
So ½ x base x height = ½ x 6 x 10 = 30 square centimeters
In these examples, the implementation of the basic formulas given makes it much easier to find the area of regular polygons. I'm talking about polygons. This covers the basics of finding the area of regular polygons.
