# Decagon shape, definition, formula, examples. (2023)

In geometry, a decagon is known as a ten-sided polygon or decagon. The sum of the interior angles of a simple decagon is 1440° and the sum of the exterior angles of a decagon is 360°.

 1 decagon meaning 2 the decagon type 3 decagon properties 4 decagon formulas 5 Decagon FAQ

## decagon meaning

A decagon is a decagon with ten sides.Polygonwith ten corners and ten angles. Therefore, a decagon shape can be defined as a polygon with ten sides, ten interior angles, and ten vertices. Based on the sides of a decagon, they are roughly classified into regular and irregular decagons. A normal decagon has 35diagonalsand 8 triangles. The location of these diagonals andtriangulosit will be explained in later sections of this article.

## the decagon type

Decagons can be classified as regular and irregular decagons based on the measures of the lengths of the sides and the angles. There are three possible classifications of decagons, detailed below:

• Regular and Irregular Decagons
• convex and concave decagons
• simple and complex decagons

### regular decagon

A regular decagon is a polygon with 10 equal sides and 10 vertices. The sides and angles of a regular decagon are congruent. The characteristics of a regular decagon are:

• All sides are the same length and allStoreare equal in size in a regular decagon.
• Each interior angle in a regular decagon measures 144°, while each exterior angle measures 36°.

### irregular toenail

An irregular decagon does not have equal sides or equal angles. At least two sides and angles are differentMeasurement🇧🇷 Take a look at the images below that show irregular decagons.

(Video) Decagon Shape | Polygon Shape |

### convex and concave decagons

Like any other polygon, it can also be decagons.convexand concave. A convex decagon bulges out if all interior angles are less than 180°. While concave decagons are notched (a deep notch). In the case of concave decagons, at least one of the interior angles is greater than 180°.

### simple and complex decagons

Simple decagons refer to decagons without intersecting sides. They follow all the regular decagon rules mentioned above. While complex decagons refer to decagons that intersect each other and have extra spaces inside. They do not follow any prescribed decagon rule regarding their interior angles and their sums.

## decagon properties

Some of the important properties of decagons are listed here.

• The sum of the interior angles is 1440°.
• The sum of the dimensions of the exterior angle is 360°.
• The central angle of a regular decagon is 36 degrees.
• A decagon has 35 diagonals.
• There are 8 triangles in a decagon.

### Sum of the interior angles of the decagon

To find the sum of the interior angles of a decagon, first divide it into triangles. There are eight triangles in a regular decagon. We know that the sum of the angles of any triangle is 180°. So 180° × 8 = 1440°. Therefore, the sum of all the interior angles of a decagon is 1440°.

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We know that the number of sides of a decagon is 10. So we divide the total of the interior angles by 10

1440° ÷ 10 = 144°

Therefore, an interior angle of a regular decagon is 144°. And the sum of all the interior angles of a decagon is 1440°.

### Measure of the central angles of a regular decagon

To find the measure of the central angle of a regular decagon, we need to draw a circle in the middle. A circle makes 360°. Divide that by ten, because a decagon has 10 sides. 360° ÷ 10 = 36°. Thus, the measure of the central angle of a regular decagon is 36°.

### decagon diagonals

A diagonal is a line that can be drawn from one vertex to another. The number of diagonals in a polygon is calculated by: n(n−3) ÷ 2. In the decagon, n is the number of sides, which is equal to 10, so n=10. Now we have,
n(n−3) ÷ 2 = 10(10−3) ÷ 2
So the number of diagonals in a decagon is 35.

### Decagon has 8 triangles

By joining avertex8 triangles are formed at the remaining corner points of the decagon. If one connects all the vertices independently, 80 (8×10) triangles are formed. Take a look at the image below which shows the diagonals and triangles of a decagon.

(Video) Find the Area of a regular #DECAGON | #Polygons | #Geometry|

## decagon formula

Like other shapes, a regular decagon has the formula for calculating perimeter and area. The formulas are listed below:

The formula to find thearea of ​​a decagonis $$\dfrac{5a^2}{2} \times \sqrt{5 + 2\sqrt{5}}$$, where a is the length of the side of the decagon.

The formula for finding the perimeter of a regular decagon is 10 times one side, or 10 × n, where n is the length of the side of the decagon (since all sides are equal and the total number of sides is 10). Given an irregular decagon, we can simply add the lengths of the sides to find the perimeter.

important notes

• A decagon has ten sides.
• The sum of the interior angles of a decagon is 1440°.
• The sum of the exterior angles of a decagon is 360°.
• A regular decagon has 35 diagonals.
• Decagons can be classified as regular, irregular, convex, concave, simple, and complex.

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## Decagon FAQ

### What is a decagon in geometry?

A decagon can be recognized as a polygon with 10 sides, 10 interior angles, and 10 vertices. The decagon can be regular and irregular. In a regular decagon, all sides are equal. The irregular decagon has unequal sides.

### How do you find the area of ​​a decagon?

The formula to find the area of ​​a regular decagon is 5a2/2 × $$\sqrt{5 + 2\sqrt{5}}}$$, where a is the length of the side of the decagon. If we know the length of a side of a regular decagon, we can use this formula to find the area. There is no formula for finding the area of ​​an irregular decagon, but we can break it down into triangles and try to find the area of ​​all the triangles and put them together.

### How many sides does a decagon have?

According to the properties of a decagon, the total number of sides is 10, formed by connecting 10 vertices. Since there are only 10 sides and 10 corners, the number of interior and exterior angles formed by the 10 sides is also 10.

### How many vertices and diagonals does a regular decagon have?

A regular decagon has 10 corners and 35 diagonals. The diagonals of a decagon are found using the formula n(n-3) ÷ 2, where n is a side number of 10. Therefore 10(10-3) ÷ 2 = 35.

### What are the exterior angles of a regular decagon?

The exterior angles of a decagon are the exterior angles formed by two sides joined by a vertex of a decagon. Each exterior angle is adjacent to the corresponding interior angle and forms 180 degrees at the vertex of the decagon. In a regular decagon all angles are equal. The sum of all the exterior angles of a regular decagon is 360°. Since the number of sides in a decagon is 10. Therefore, each exterior angle is equal to 36° (360° ÷ 10 = 36°).

### What is the sum of the interior angles of a decagon?

The sum of all the interior angles of a decagon is 1440°. There is a formula to find the sum of the interior angles of a polygon with n sides [(n-2)(180)], where n is equal to the number of sides. So the sum of the interior angles of the decagon = (10-2) × 180° = 1440°. Also, the measure of each interior angle in a regular decagon can be found by dividing the sum and the total number of sides in the decagon ⇒ 1.440/10 = 144°.

### What do you call a figure with 10 sides?

A decagon is known as a ten-sided shape or polygon with ten vertices and ten angles. When any shape is formed by joining 10 sides, it is called a decagon.

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## FAQs

### What is decagon shape examples? ›

We also define decagon as the polygon having ten sides, ten interior angles, ten exterior angles, and ten vertices. For example, the shape of a star has 10 sides, 10 vertices, which clearly indicates that the star is a decagon.

What is the definition of decagon shape? ›

In geometry, a polygon having ten sides or a ten-sided polygon is called a decagon or ten-gon. It also has ten vertices and ten angles.

What is a decagon for kids? ›

A decagon is a ten-sided two-dimensional (2D) shape. This means it only has height and width (you can't hold it as it has no depth).

What is the solution of decagon? ›

The formula to find the area of a decagon is 5a22×√5+2√5 5 a 2 2 × 5 + 2 5 , where a is the measurement of the side-length of the decagon. The formula to find the perimeter of a regular decagon is 10 times of a side or 10 × n, where n is the side-length of the decagon (as all sides are equal and total sides are 10).

What are 5 shapes examples? ›

Circle, Triangle, Square, Rectangle, Kite, Trapezium, Parallelogram, Rhombus and different types of polygons are the 2-d shapes. Cube, Cuboid, Sphere, Cone and Cylinder are the basic three-dimensional shapes.

How do you find the area of a decagon? ›

What is the Formula to Find the Area of a Regular Decagon? The formula to determine the value of the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 , where 'a' is the side length of the decagon.

How does a decagon work? ›

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440° . An irregular decagon has sides and angles that are not all equal or congruent.

What is the formula of dodecagon? ›

The formula for finding the area of a regular dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area of the dodecagon, s = the length of its side. For example, if the side of a regular dodecagon measures 8 units, the area of this dodecagon will be: A = 3 × ( 2 + √3 ) × s2 .

Why is it called a decagon? ›

The word decagon comes from Greek roots, deka, or "ten," and gōnia, "angle or corner." Any ten-sided shape can be called a decagon, whether it's a street sign or the doodle you draw in your notebook during math class.

What are the angles in a decagon? ›

A regular decagon has all sides of equal length and each internal angle will always be equal to 144°.

### How many triangles are in a decagon? ›

Therefore, the total number of triangles that can be formed in a decagon are 120 . Note: In decagon as there are no collinear points or vertices. Hence, from all these points we can choose any three at a time to form a triangle.

How many sides does a decagon have answer? ›

A decagon is a 10-sided polygon with 10 interior angles and 10 vertices.

How do you find the volume of a decagon? ›

The volume of a decagonal prism is the area of the decagonal base times the height.

Can you give me an example of shapes? ›

Everything we see in the world around us has a shape. We can find different basic shapes such as the two-dimensional square, rectangle, and oval or the three-dimensional rectangular prism, cylinder, and sphere in the objects we see around us.

What shape has 7 sides? ›

A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended.

What is shape with example? ›

A shape is defined for an object or any external surface or boundary, apart from other properties such as colour or material type. For example, a blue ball, made up of rubber materials is round in shape.

Does a decagon have 10 equal sides? ›

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440°. An irregular decagon has sides and angles that are not all equal or congruent.

How do you find the area of the sides? ›

The sides can be found by taking the square root of the area.

What is an example of a dodecagon? ›

The regular dodecagon features prominently in many buildings. The Torre del Oro is a dodecagonal military watchtower in Seville, southern Spain, built by the Almohad dynasty. The early thirteenth century Vera Cruz church in Segovia, Spain is dodecagonal.

What is a 12 polygon called? ›

A dodecagon is a 12-sided polygon.

### How much is in a decagon? ›

A decagon has ten straight sides and ten vertices (corners). It has ten angles inside it that add up to 1440°.

How many faces does a decagon have? ›

The decagonal prism has 12 faces, 30 edges, and 20 vertices, so, it is a dodecahedron (while the term is usually applied to regular dodecahedron or rhombic dodecahedron.).

How many edges does a decagon have? ›

Is a star a decagon? ›

In geometry, a star shape or a star polygon is a type of non-convex polygon. This is a shape where all the angles inside the polygon are less than 180 degrees. Most commonly, star shapes are also a type of decagon.

Does a decagon add up to 360? ›

Regular Decagons – These decagons have sides of equal length and have equal angles. The interior angles add up to 1440° and the exterior angles add up to 360 degrees.

What shape has 11 sides? ›

A hendecagon is an 11-sided polygon, also variously known as an undecagon or unidecagon.

How many pairs are in a decagon? ›

Number of sides in do-decagon = 12. Download the app to view unlimited solutions on app.

What is the formula for volume? ›

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height. How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'.

What are 3 examples of a polygon? ›

Triangles, hexagons, pentagons, and quadrilaterals are all examples of polygons. The name gives an indication of how many sides the shape has. For example, a triangle consists of three sides while a quadrilateral consists of four sides.

What is an everyday example of a dodecagon? ›

Examples in use

A cross is a dodecagon, as is the logo for the Chevrolet automobile division.

### What shape has 7 sides called? ›

A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended.

What shape has 12 sides? ›

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with all sides the same length is a regular polygon known as a regular dodecagon.

What is polygon formula? ›

Polygon Formula

The important polygon formulas are: The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n. The measure of exterior angles of a regular n-sided polygon = 360°/n.

What is polygon explain the 10 types with example? ›

A Polygon is made up of only straight lines. Each straight line in a Polygon is called its side. A Polygon is classified based on its sides like a triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, and decagon according as it contains (3, 4, 5, 6, 7, 8, 9) and (10) sides, respectively.

What is polygon definition for kids? ›

Any closed two-dimensional shape with three or more sides is called a polygon. Triangles and squares are polygons, as well as more complicated shapes like a twelve-sided dodecagon.

What is the meaning of dodecagon in math terms? ›

A dodecagon is a closed figure that has 12 sides and 12 angles. It has 12 vertices, each of which is connected to two sides. See the below figure which is an example of a dodecagon. Depending on the sides and angles a dodecagon can be a regular or irregular polygon and a convex or concave polygon.

What is true about decagon *? ›

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440° . An irregular decagon has sides and angles that are not all equal or congruent.

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