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# Perimeter of a Polygon Formula | Diagonal & Area of Regular Polygon

## Polygon Formula

Polygon is the two-dimensional shape that is formed by the straight lines. The polygon with a minimum number of sides is named the triangle. Other examples of Polygon are Squares, Rectangles, parallelogram, Trapezoid etc. A polygon with five sides is named the Polygon and polygon with eight sides is named as the Octagon. If the length of all sides is equal then this is a regular polygon otherwise it would an irregular polygon. So, how to calculate the perimeter of a polygon in mathematics.

• The Perimeter is the sum total of all sides of a Polygon.
• The Perimeter of rhombus and square is always equal.
• The Perimeter of parallelogram and rectangle is also the same.
• The Perimeter of a polygon with more than 6 sides can be found by plug-in values into perimeter formula.

Polygon formula to find area:

$\large Area\;of\;a\;regular\;polygon=\frac{1}{2}n\; sin\left(\frac{360^{\circ}}{n}\right)s^{2}$

Polygon formula to find interior angles:

$\large Interior\;angle\;of\;a\;regular\;polygon=\left(n-2\right)180^{\circ}$

Polygon formula to find the triangles:

$\large Interior\;of\;triangles\;in\;a\;polygon=\left(n-2\right)$

Where, n is the number of sides and S is the length from center to corner.

### The perimeter of A Polygon Formula

A regular polygon is a polygon with all its sides equal and equal angles too. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n – 2) degrees. The Perimeter of a Regular Polygon in mathematics is given by:

$\ p = n\times s$

Where n is the number of sides and s is the length of each side. At the same time, the irregular polygon is the shape whose sides and angles are not equal. The Perimeter of an irregular shape is calculated by adding the length of each side together.

### Area of Regular Polygon Formula

When you would look around carefully then regular polygons can be seen everywhere. To understand the regular polygon deeply, you should read the terminologies associated with it. The first thing is that you should know the number of sides of the regular polygon that is generally denoted by the alphabet n.

Based on the number of sides, you could always check which type of polygon are you using. For example, of the value of n is eight then this is an Octagon. Now you should know the length of each side to calculate the perimeter or the area of a Polygon.

Another popular measurement is the Apothem, the distance from the center of a regular polygon to the mid of any of its sides. When you will draw a line from each of the corners of a regular polygon towards the center then we could break down the polygon into a smaller number of triangles. After this, the Apothem can be linked to the height of each of the small triangle. The formula of area of a regular polygon in mathematics is given as –

$\ A = \frac{l^{2}n}{4tan(\frac{\pi }{n})}$

Where,
l is the side length
n is the number of sides

### Diagonal of A Polygon Formula

The diagonal of a polygon is the line segment from one corner to another but it will not include the edges. If there is one n sided polygon then its diagonal could be given as –

$\ Diagonal\;of\;a\;Polygon = \frac{n(n-3)}{2}$
where n is the number of polygon sides.

For example, A square has 2 diagonals and an octagon has 20 diagonals.