Polygons Calculator

Polygons Calculator Image to Crop

Enter 2 values

Given a polygon with 5 sides (n)

Each with length (s) of 7

Calculate the Perimeter (P) and Area (A)

Calculate Perimeter:

P = n x s

P = 5 x 7

P = 35

Calculate Area:

A =	s2n
	4tan(π/n)

A =	725
	4tan(3.1415926535898/5)

A =	49 x 5
	4tan(0.62831853071796)

A =	245
	4(0.010966666713617)

A =	245
	0.043866666854469

A = 5585.1063590677

Calculate Sum of the Interior Angles:

Interior Angle Sum = (n - 2) x 180°

Interior Angle Sum = (5 - 2) x 180°

Interior Angle Sum = (3) x 180°

Interior Angle Sum = 540°

Calculate the number of diagonals

Diagonals =	n(n - 3)
	2

Diagonals =	5(5 - 3)
	2

Diagonals =	5(2)
	2

Diagonals =	10
	2

Diagonals = 5

Calculate 1 vertex diagonals

1 vertex Diagonals = n - 3
1 vertex Diagonals = 5 - 3
1 vertex Diagonals = 2

Calculate 1 vertex triangles

Triangles = N - 2
Triangles = 5 - 2
Triangles = 3

Determine polygon type

Since the polygon has 5 sides, it is a pentagon

Final Answers

P = 35
A = 5585.1063590677
Interior Angle Sum = 540
Diagonals = 5
1 Vertex Diagonals = 2
Triangles = 3
Polygon Type = pentagon

What is the Answer?

P = 35
A = 5585.1063590677
Interior Angle Sum = 540
Diagonals = 5
1 Vertex Diagonals = 2
Triangles = 3
Polygon Type = pentagon

How does the Polygons Calculator work?

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon. This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.
This calculator has 5 inputs.

What 13 formulas are used for the Polygons Calculator?

P = n x s
A = s2n/4tan(π/n)
Interior Angle Sum = (n - 2) x 180°
Diagonals = n(n - 3)/2
1 vertex Diagonals = n - 3
Triangles = N - 2
5 sides = Pentagon
6 sides = Hexagon
7 sides = Heptagon
8 sides = Octagon
9 sides = Nonagon
10 sides = Decagon

For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Polygons Calculator?

apothema line segment from the center to the midpoint of one of its sidesareaNumber of square units covering the shapediagonalline segment that goes from one corner to another, but is not an edgeperimeterThe distance around a shape or objectpolygonA plane figure bounded by a set of straight linesradiusDistance from the center of a circle to the edge
C/2π

ZinBlog