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 - 31 vertex Diagonals = 10 - 3
1 vertex Diagonals = 7
Calculate 1 vertex triangles
Triangles = N - 2Triangles = 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
Diagonals = 35
1 Vertex Diagonals = 7
Triangles = 8
Polygon Type = decagon
Common Core State Standards In This Lesson
3.MD.D.8
What is the Answer?
Interior Angle Sum = 1440
Diagonals = 35
1 Vertex Diagonals = 7
Triangles = 8
Polygon Type = decagon
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.
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
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
What 6 concepts are covered in the Polygons Calculator?
- apothem
- a line segment from the center to the midpoint of one of its sides
- area
- Number of square units covering the shape
- diagonal
- line segment that goes from one corner to another, but is not an edge
- perimeter
- The distance around a shape or object
- polygon
- A plane figure bounded by a set of straight lines
- radius
- Distance from the center of a circle to the edge
C/2π
