Polygons Calculator ·

26 Jul 2024, 00:00

Polygons Calculator Image to Crop

Enter 2 values

Calculate Sum of the Interior Angles:

Interior Angle Sum = (n - 2) x 180°

Interior Angle Sum = (10 - 2) x 180°

Interior Angle Sum = (8) x 180°

Interior Angle Sum = 1440°

Calculate the number of diagonals

Diagonals =	n(n - 3)
	2

Diagonals =	10(10 - 3)
	2

Diagonals =	10(7)
	2

Diagonals =	70
	2

Diagonals = 35

Calculate 1 vertex diagonals

1 vertex Diagonals = n - 3
1 vertex Diagonals = 10 - 3
1 vertex Diagonals = 7

Calculate 1 vertex triangles

Triangles = N - 2
Triangles = 10 - 2
Triangles = 8

Determine polygon type

Since the polygon has 10 sides, it is a decagon

Final Answers

Interior Angle Sum = 1440
Diagonals = 35
1 Vertex Diagonals = 7
Triangles = 8
Polygon Type = decagon

What is the Answer?

Interior Angle Sum = 1440
Diagonals = 35
1 Vertex Diagonals = 7
Triangles = 8
Polygon Type = decagon

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

Polygons Calculator

Interior Angle Sum = (n - 2) x 180 Interior Angle Sum = (10 - 2) x 180 Interior Angle Sum = (8) x 180 Interior Angle Sum = 1440 Diagonals = 35 Since the polygon has 10 sides, it is a decagon Interior Angle Sum = 1440Diagonals = 351 Vertex Diagonals = 7Triangles =