In geometry, a decagon is well-known as a ten-sided polygon or ten-gon. The sum of the inner angles the a an easy decagon is 1440° and the sum of the exterior angles of a decagon is 360°.

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1.What is a Decagon?
2.Types that Decagon
3.Properties of Decagon
4.Decagon Formulas
5.Decagon Examples
6.Practice Questions
7.FAQs ~ above Decagon

A decagon is a ten-sided polygon v ten vertices and also ten angles.Thus, a decagon shape can be defined as a polygon having ten sides, ten internal angles, and ten vertices. Based upon the sides of a decagon, castle are generally classified into continuous decagons and also irregular decagons. A constant decagon has actually 35 diagonals and 8 triangles. The location of these diagonals and also triangles is explained in the later sections of this article.


Decagons deserve to be categorized together regular and irregular decagons based upon side-length and also angle measurements. There room three possible classifications the decagon that are provided below:

Regular and also Irregular DecagonsConvex and Concave DecagonsSimple and complex Decagons

Regular Decagon

A continuous decagon is a polygon follow me with10 equal sides and 10 vertices.The sides and also angles are congruent in a continuous decagon. The features of a consistent decagon are:

Each interior angle in regular decagon procedures 144º, while every exterior angle measures 36º.

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Irregular Decagon

An irregular decagon walk not have equal sides and also angles. At the very least two sides and also angles are different in measurement. Look at the pictures given listed below showing rarely often, rarely decagons.

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Convex and Concave Decagons

Like any type of other polygon, decagons also can be convex and also concave. A convex decagon bulges exterior as all the internal angles space lesser than 180°. When concave decagons have indentations (a deep recess). At the very least one that the interior angles is greater than 180° in concave decagons.

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Simple and facility Decagons

Simple decagons describe decagons with no political parties crossing themselves. Lock follow every one of the above said consistent decagon rules. While complex decagons refer to decagons that are self-intersecting and also have additional interior spaces. They do not strictly follow any type of prescribed rule of decagons concerning their inner angles and also their sums.

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Properties of Decagon


Some that the necessary properties the decagons are listed here.

The amount of the interior angles is 1440°.The amount of the measurements of the exterior edge is 360°.The main angle measures 36 degrees in the instance of a continuous decagon.There are 35 diagonals in a decagon.There are 8 triangle in a decagon.

Sum that the interior Angles of Decagon

To uncover the amount of the internal angles the a decagon, first, divide it into triangles. There room eight triangles in a constant decagon. We understand that the amount of the angle in each triangle is 180°. Thus,180° × 8 = 1440°. Therefore, the sum of every the inner angles that a decagon is1440°.We understand that the number of sides of a decagon is 10. Hence, we divide the total sum the the inner angles through 101440° ÷ 10 = 144°Thus, one inner angle the a constant decagon shape is 144°. And, the sum of every the inner angles the a decagon is 1440°.

Measure of the main Angles the a regular Decagon

To discover the measure of the central angle the a continuous decagon, we should drawa circle in the middle. A circle creates 360°.Divide this through ten, due to the fact that a decagonhas 10 sides. 360° ÷ 10 = 36°. Thus, the measure up of the central angle of a constant decagon is36°.

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Decagon Diagonals

A diagonal is a heat that can be attracted from one vertexto another. The variety of diagonals that a polygon is calculated by:n(n−3) ÷ 2. In decagon, n is the variety of sides which is equal to 10, therefore n=10. Now we get,n(n−3) ÷ 2 = 10(10−3) ÷ 2Thus, the number of diagonals in a decagon is 35.

Decagon has actually 8 Triangles

By joining one vertex come the staying vertices of the decagon,8 triangles will be formed. Through joiningall the vertices independently to each other, climate 80 triangle (8×10) will be formed. Look at the image offered below, reflecting diagonals and triangles of a decagon.

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Decagon Formulas


Like various other shapes, a continuous decagon additionally has the formula to calculateperimeter andarea. The formulas are mentioned below:

The formula to find the area of a decagon is \(\dfrac5a^22 \times\sqrt5 + 2\sqrt5\),where ais the measure of the side-length of the decagon.

The formula to discover the perimeter of a continual decagon is 10 times of a next or 10 × n, wherein n is the side-length of the decagon (as every sides space equal and total sides space 10). In the situation of an rarely often, rarely decagon, we can simply add the next lengths to find the perimeter.

Important Notes

A decagon has ten sides.The sum of the interior angles of a decagon is1440°.The sum of the exterior angle of a decagon is360°.A continuous decagon has actually 35 diagonals.Decagons have the right to be classified together regular, irregular, convex, concave, simple, and also complex.

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