In geometry, a decagon is well-known as a ten-sided polygon or ten-gon. The amount of the interior angles of a simple 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 the Decagon
3.Properties the Decagon
4.Decagon Formulas
5.Decagon Examples
6.Practice Questions
7.FAQs ~ above Decagon

A decagon is a ten-sided polygon with ten vertices and ten angles.Thus, a decagon shape have the right to be characterized as a polygon having ten sides, ten internal angles, and ten vertices. Based upon the political parties of a decagon, they are generally classified into consistent decagons and irregular decagons. A regular decagon has actually 35 diagonals and also 8 triangles. The ar of these diagonals and also triangles is defined in the later sections that this article.


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

Regular and also Irregular DecagonsConvex and Concave DecagonsSimple and facility Decagons

Regular Decagon

A regular decagon is a polygon along with10 same sides and 10 vertices.The sides and also angles room congruent in a constant decagon. The features of a constant decagon are:

Each inner angle in continual decagon steps 144º, while every exterior angle measures 36º.

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Irregular Decagon

An rarely often, rarely decagon does not have equal sides and angles. At least two sides and angles are various in measurement. Look at the images given below showing irregular decagons.

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Convex and also Concave Decagons

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

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Simple and complicated Decagons

Simple decagons describe decagons v no political parties crossing themselves. Castle follow every one of the above said continual decagon rules. While complicated decagons describe decagons that room self-intersecting and have additional interior spaces. They perform not strictly follow any kind of prescribed rule of decagons about their inner angles and also their sums.

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Properties the Decagon


Some of the crucial properties the decagons are noted here.

The sum of the interior angles is 1440°.The sum of the dimensions of the exterior edge is 360°.The central angle measures 36 levels in the instance of a consistent decagon.There room 35 diagonals in a decagon.There space 8 triangles in a decagon.

Sum the the inner Angles that Decagon

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

Measure the the main Angles that a regular Decagon

To uncover the measure up of the central angle the a constant decagon, we have to drawa circle 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 the a continuous decagon is36°.

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Decagon Diagonals

A diagonal is a heat that deserve to be drawn from one vertexto another. The number of diagonals the a polygon is calculated by:n(n−3) ÷ 2. In decagon, n is the number of sides which is same to 10, for this reason 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 authorized one vertex to the remaining vertices that the decagon,8 triangles will certainly be formed. By joiningall the vertices independently to each other, then 80 triangle (8×10) will certainly be formed. Look at the image given below, reflecting diagonals and also triangles that a decagon.

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Decagon Formulas


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

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

The formula to discover the perimeter the a constant decagon is 10 time of a side or 10 × n, whereby n is the side-length that the decagon (as all sides room equal and also total sides room 10). In the situation of an irregular decagon, we have the right to simply include the next lengths to discover the perimeter.

Important Notes

A decagon has actually ten sides.The amount of the inner angles of a decagon is1440°.The amount of the exterior angle of a decagon is360°.A continual decagon has 35 diagonals.Decagons deserve to be classified together regular, irregular, convex, concave, simple, and also complex.

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