What Is A Nonagon Shape
Nonagon
Nonagon is a polygon that has nine sides, ix interior angles and 9 exterior angles. A nonagon has 27 diagonals and the sum of the interior angles of a nonagon is 1260°. A nonagon shape tin be regular or irregular depending upon the sides and angles. Permit us learn more about the nonagon shape.
| 1. | What is a Nonagon Shape? |
| two. | Nonagon Sides |
| 3. | Regular Nonagon |
| 4. | Sum of Interior Angles of a Nonagon |
| 5. | FAQs on Nonagon |
What is a Nonagon Shape?
A nonagon is a nine-sided geometrical figure which can be regular, irregular, convex or concave depending upon its sides and interior angles. Detect the figure given below to see what a nonagon looks similar.
Nonagon Sides
As seen in the figure given in a higher place, a nonagon has nine sides and the name 'Nonagon' was derived from the Latin words 'nonus' and 'gon' which mean a polygon with ix sides. These 9 sides of a nonagon can be equal or of different measures.
Regular Nonagon
A regular nonagon is one in which all the 9 sides are of equal length and the 9 interior angles are of equal mensurate. On the other hand, when the sides of a nonagon are of diff lengths and the angles are of dissimilar measure, information technology is chosen an irregular nonagon.
Properties of a Regular Nonagon
The post-obit points show the backdrop of a regular nonagon.
- In a regular nonagon, all the sides are of equal length, and all the interior angles are of equal measure.
- The sum of the interior angles of a regular nonagon is 1260° and the sum of the exterior angles is 360°.
- Each interior angle of a regular nonagon measures 140°.
Observe the following figure which shows a regular nonagon and an irregular nonagon.
Convex Nonagon and Concave Nonagon
A convex nonagon has the following properties.
- A convex nonagon is i in which all the interior angles measure less than 180°.
- Since each interior angle of a convex nonagon is less than 180°, convex nonagons seem to bulge outwards.
A concave nonagon has the post-obit backdrop.
- A concave nonagon is 1 in which at least one interior angle is a reflex angle.
- In a concave nonagon, the vertices of a concave nonagon can exist inwards which gives it that peculiar shape.
Observe the figure given below which shows a convex nonagon and a concave nonagon shape.
Nonagon Angles
There are ix interior angles and nine respective outside angles in a nonagon. Observe the figure given beneath which shows the interior angles and the exterior bending of a regular nonagon. Let us read virtually them in detail.
Nonagon Interior Angles
Each interior bending of a regular nonagon measures 140°. This can exist calculated using the formula for the interior angles of a regular polygon. Interior angle of a regular polygon =\(\frac{180n–360} {n}\), where due north = the number of sides of the polygon. In a nonagon, n = 9. After substituting this value of 'n' in the formula, nosotros go \(\begin{align} \frac{180(9)–360} {9} = 140^\circ \end{marshal}\)
Sum of Interior Angles of a Nonagon
The sum of the interior angles of a nonagon is ever 1260°. This sum remains the same irrespective of the nonagon being a regular or an irregular nonagon and this can be calculated using the formula, Sum of interior angles of a polygon = (n - ii) × 180°, where 'northward' = number of sides of the polygon. Here, after substituting the value of northward = nine, we get, Sum of interior angles of a polygon = (9 - 2) × 180° = 1260°.
Nonagon Outside Angles
Each exterior angle of a regular nonagon measures xl°. If we observe the figure given above, nosotros can come across that the outside angle and interior angle form a linear pair of angles, which means they sum up to 180°. Hence, each exterior angle of a regular nonagon will be 180° - 140° = 40°. The sum of the exterior angles of a nonagon is 360°.
Properties of Nonagon
The post-obit properties of a nonagon help to distinguish it from other polygons.
- A nonagon is a polygon with 9 sides, 9 interior angles, and nine outside angles.
- The interior angles of a nonagon sum up to 1260°
- A nonagon has 27 diagonals.
Nonagon Diagonals
There are 27 diagonals in a nonagon. These diagonals are drawn past joining its not-adjacent vertices and the total number of diagonals in a nonagon can be calculated using the formula, Number of diagonals in a polygon = 1/two × due north × (due north-3), where n = number of sides in the polygon. Here, northward = 9. After substituting this value of n = 9 in the formula we get, Number of diagonals in a polygon: i/2 × due north × (n-iii) = 1/ii × ix × (9-three) = 27. Therefore, a nonagon has 27 diagonals.
Perimeter of Nonagon
The perimeter of a polygon is the total length of its purlieus. So, in order to find the perimeter of a nonagon, we need to know the length of all 9 sides. The sum of all the sides gives the perimeter of a nonagon. In example of a regular nonagon, all the sides are of equal length, so nosotros can multiply the length of one side past 9 to get the perimeter. These formulas tin can exist expressed as follows.
Perimeter of a nonagon = Sum of all its sides
Perimeter of a regular nonagon = 9a (Where 'a' is the length of ane side of the nonagon)
☛ Related Articles
- Types of Polygon
- Pentagon
- Hexagon
- Heptagon
- Octagon
- Decagon
- Dodecagon
- Dodecahedron
Examples on Nonagon
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Practice Questions on Nonagon
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FAQs on Nonagon
What is a Nonagon Shape?
Nonagon is a polygon with nine sides, nine vertices and ix interior angles. A nonagon tin can exist regular, irregular, convex or concave depending upon its sides and interior angles.
What is a Regular Nonagon?
A regular nonagon is 1 in which all the sides are of equal length and all the interior angles are of equal mensurate. This means each interior angle of a regular nonagon is equal to 140°, and therefore, each respective outside angle is forty°.
What is the Sum of the Interior Angles of a Nonagon?
The sum of the interior angles of a nonagon is 1260°. This can be calculated with the assist of the formula, Sum of interior angles of a polygon = (due north - 2) × 180°, where 'n' = number of sides of the polygon. After substituting the value of n = 9, nosotros get, Sum of interior angles of a polygon = (ix - two) × 180° = 1260°.
What is the Interior Angle of a Nonagon?
The interior bending of a nonagon is formed within the nonagon. Each interior angle of a regular nonagon measures 140°. This tin can be calculated using the formula, Interior angle of a regular polygon =\(\frac{180n–360} {northward}\), where n = the number of sides of the polygon. Since a nonagon has 9 sides, n = ix. After substituting this value of 'due north' in the formula, we get \(\begin{marshal} \frac{180(9)–360} {9} = 140^\circ \cease{align}\)
What is the Exterior Angle of a Nonagon?
Each exterior angle of a regular nonagon measures forty°. When whatsoever side of a nonagon is extended outwards, the angle that is formed with this side and its adjacent side is chosen the exterior angle of the nonagon. Since each exterior bending forms a linear pair with its corresponding interior angle, information technology means they both sum up to 180°. Therefore, each exterior bending of a regular nonagon is, 180° - 140° = 40°. The sum of the exterior angles of a nonagon is 360°.
How many Sides are there in a Nonagon?
At that place are 9 sides in a nonagon. A nonagon tin be regular, irregular, convex, or concave depending on the length of its sides and angles.
How many Triangles are there in a Nonagon?
vii triangles tin exist drawn in a nonagon. A nonagon can be separate into triangles with the assist of its diagonals that are drawn from its vertices. The number of triangles that are created by these diagonals, tin be calculated with the formula: (n - 2), where north = the number of sides. In this case, n = 9. So, later on substituting this value in the formula nosotros get, 9 - ii = vii. Therefore, 7 triangles can be formed in nonagon.
What is a Convex Nonagon?
A convex nonagon is one in which all the interior angles measure less than 180°. Since each interior bending of a convex nonagon is less than 180°, convex nonagons seem to bulge outwards.
What Is A Nonagon Shape,
Source: https://www.cuemath.com/geometry/nonagon/
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