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

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1.What is a Decagon?
2.Types the Decagon
3.Properties the Decagon
4.Decagon Formulas
5.Decagon Examples
6.Practice Questions
7.FAQs top top Decagon

A decagon is a ten-sided polygon v ten vertices and ten angles.Thus, a decagon shape deserve to be defined as a polygon having ten sides, ten interior angles, and also ten vertices. Based upon the sides of a decagon, they are generally classified into continuous decagons and irregular decagons. A continuous decagon has 35 diagonals and 8 triangles. The ar of these diagonals and triangles is defined in the later sections the this article.


Decagons can be categorized together regular and irregular decagons based on side-length and angle measurements. There are three possible classifications of decagon that are given below:

Regular and Irregular DecagonsConvex and also Concave DecagonsSimple and complex Decagons

Regular Decagon

A consistent decagon is a polygon follow me with10 same sides and also 10 vertices.The sides and also angles space congruent in a continual decagon. The characteristics of a regular decagon are:

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

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Irregular Decagon

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

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Convex and Concave Decagons

Like any kind of other polygon, decagons additionally can be convex and also concave. A convex decagon bulges outside as all the inner angles room lesser 보다 180°. When concave decagons have actually indentations (a deep recess). At the very least one the the inner angles is greater than 180° in concave decagons.

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Simple and complex Decagons

Simple decagons refer to decagons with no sides crossing themselves. They follow every one of the above said consistent decagon rules. While complex decagons describe decagons that room self-intersecting and have additional interior spaces. They perform not strict follow any type of prescribed rule of decagons regarding their inner angles and their sums.

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Properties that Decagon


Some the the essential properties of decagons are noted here.

The sum of the internal angles is 1440°.The sum of the dimensions of the exterior angle is 360°.The main angle actions 36 degrees in the situation of a continual decagon.There space 35 diagonals in a decagon.There are 8 triangles in a decagon.

Sum of the interior Angles of Decagon

To find the amount of the inner angles the a decagon, first, division it right into triangles. There space eight triangle in a continuous decagon. We understand that the amount of the angle in each triangle is 180°. Thus,180° × 8 = 1440°. Therefore, the amount of every the interior angles the a decagon is1440°.We understand that the variety of sides that a decagon is 10. Hence, we division the full sum the the interior angles through 101440° ÷ 10 = 144°Thus, one inner angle the a continual decagon shape is 144°. And, the sum of every the interior angles of a decagon is 1440°.

Measure the the main Angles of a continual Decagon

To discover the measure of the main angle of a consistent decagon, we have to drawa one in the middle. A circle develops 360°.Divide this by ten, because a decagonhas 10 sides. 360° ÷ 10 = 36°. Thus, the measure up of the central angle of a continuous decagon is36°.

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Decagon Diagonals

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

Decagon has actually 8 Triangles

By authorized one vertex to the continuing to be vertices the the decagon,8 triangles will certainly be formed. By joiningall the vertices independently to every other, then 80 triangle (8×10) will certainly be formed. Look at the image offered below, reflecting diagonals and also triangles the a decagon.

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Decagon Formulas


Like other shapes, a constant decagon additionally has the formula come calculateperimeter andarea. The recipe are mentioned below:

The formula to find the area that a decagon is (dfrac5a^22 imessqrt5 + 2sqrt5),where ais the measurement of the side-length the the decagon.

The formula to uncover the perimeter that a continual decagon is 10 time of a side or 10 × n, where n is the side-length of the decagon (as every sides room equal and also total sides space 10). In the situation of an irregular decagon, we deserve to simply include the next lengths to uncover the perimeter.

Important Notes

A decagon has actually ten sides.The amount of the inner angles of a decagon is1440°.The sum of the exterior angles of a decagon is360°.A consistent decagon has actually 35 diagonals.Decagons can be classified as regular, irregular, convex, concave, simple, and complex.

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