Answer
A = 15
s = 1.5577124976805
P = 14.019412479124
Interior Angle sum = 1260°
Diagonals = 27
1 vertex Diagonals = 6
Triangles = 7
Sides (Edges) = 9
Faces = 1
Vertices = 9
s = 1.5577124976805
P = 14.019412479124
Interior Angle sum = 1260°
Diagonals = 27
1 vertex Diagonals = 6
Triangles = 7
Sides (Edges) = 9
Faces = 1
Vertices = 9
↓Steps Explained:↓
The Area of a nonagon is 15
Calculate side, perimeter
Calculate side:
A = 9/4s2cot(180°/9)
| s2 = | 4A |
| 9cot(180°/9) |
| s2 = | 4 x 15 |
| 9cot(20) |
| s2 = | 60 |
| 9 x 2.7474774228644 |
| s2 = | 60 |
| 24.727296805779 |
s2 = 2.42646822543
s = √2.42646822543
s = 1.5577124976805
Calculate Perimeter:
P = 9 x side
P = 9 x 1.5577124976805
P = 14.019412479124
Calculate Sum of the Interior Angles:
Interior Angle Sum = (sides - 2) x 180°
Interior Angle Sum = (9 - 2) x 180°
Interior Angle Sum = 7 x 180°
Interior Angle sum = 1260°
Calculate polygon diagonals
| Diagonals = | n(n - 3) |
| 2 |
| Diagonals = | 9(9 - 3) |
| 2 |
| Diagonals = | 9(6) |
| 2 |
| Diagonals = | 54 |
| 2 |
Diagonals = 27
Calculate 1 vertex diagonals:
1 vertex Diagonals = n - 3
1 vertex Diagonals = 9 - 3
1 vertex Diagonals = 6
Calculate triangles from one vertex:
Triangles = N - 2
Triangles = 9 - 2
Triangles = 7
Other Properties:
Sides (Edges) = 9
Faces = 1
Vertices = 9
Final Answers
A = 15s = 1.5577124976805
P = 14.019412479124
Interior Angle sum = 1260°
Diagonals = 27
1 vertex Diagonals = 6
Triangles = 7
Sides (Edges) = 9
Faces = 1
Vertices = 9
Related Calculators: Polygons | Heptagon | Octagon