Polygons Calculator
Enter 2 values
You entered pentagon
This corresponds to an 5 sided polygon
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 - 31 vertex Diagonals = 5 - 3
1 vertex Diagonals = 2
Calculate 1 vertex triangles
Triangles = N - 2Triangles = 5 - 2
Triangles = 3
Determine polygon type
Since the polygon has 5 sides, it is a pentagon
Final Answers
Interior Angle Sum = 540
Diagonals = 5
1 Vertex Diagonals = 2
Triangles = 3
Polygon Type = pentagon
What is the Answer?
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 sA = 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 edgeC/2π
Example calculations for the Polygons Calculator
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