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

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

A decagon is a ten-sided polygon through ten vertices and ten angles.Thus, a decagon shape can be characterized as a polygon having actually ten sides, ten interior angles, and ten vertices. Based on the political parties of a decagon, they are extensively classified into continuous decagons and irregular decagons. A constant decagon has 35 diagonals and also 8 triangles. The place of these diagonals and triangles is described in the later sections the this article.


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

Regular and Irregular DecagonsConvex and Concave DecagonsSimple and complicated Decagons

Regular Decagon

A regular decagon is a polygon along with10 equal sides and 10 vertices.The sides and also angles space congruent in a continuous decagon. The features of a regular decagon are:

Each interior angle in consistent decagon steps 144º, while each exterior angle actions 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 various in measurement. Look at the pictures given below showing rarely often rare decagons.

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Convex and Concave Decagons

Like any kind of other polygon, decagons also can it is in convex and concave. A convex decagon bulges outward as all the inner angles are lesser 보다 180°. While concave decagons have indentations (a deep recess). At least one the the inner angles is better than 180° in concave decagons.

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Simple and facility Decagons

Simple decagons refer to decagons v no sides crossing themselves. Castle follow all of the over said consistent decagon rules. While complex decagons refer to decagons that space self-intersecting and also have additional interior spaces. They execute not strictly follow any prescribed rule of decagons concerning their inner angles and their sums.

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Properties the Decagon


Some that the necessary properties of decagons are listed here.

The sum of the interior angles is 1440°.The sum of the measurements of the exterior edge is 360°.The main angle steps 36 levels in the instance of a regular decagon.There space 35 diagonals in a decagon.There room 8 triangle in a decagon.

Sum that the inner Angles the Decagon

To uncover the amount of the inner angles the a decagon, first, division it into triangles. There are eight triangle in a regular 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 know that the variety of sides the a decagon is 10. Hence, we divide the full sum the the internal angles through 101440° ÷ 10 = 144°Thus, one internal angle that a continuous decagon shape is 144°. And, the sum of all the internal angles the a decagon is 1440°.

Measure of the main Angles the a continual Decagon

To discover the measure of the central angle of a consistent decagon, we must drawa one in the middle. A circle creates 360°.Divide this by ten, due to the fact that a decagonhas 10 sides. 360° ÷ 10 = 36°. Thus, the measure of the main angle of a consistent decagon is36°.

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Decagon Diagonals

A diagonal line is a heat that have the right to be drawn from one vertexto another. The variety 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, so n=10. Now 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 involvement one vertex come the staying vertices that the decagon,8 triangles will certainly be formed. By joiningall the vertices separately to each other, then 80 triangles (8×10) will certainly be formed. Look in ~ the image offered below, showing diagonals and also triangles that a decagon.

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Decagon Formulas


Like various other shapes, a regular decagon also has the formula come calculateperimeter andarea. The formulas are stated below:

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

The formula to discover the perimeter that a continual decagon is 10 times of a next or 10 × n, wherein n is the side-length the the decagon (as all sides space equal and also total sides are 10). In the instance of an irregular decagon, we have the right to simply add the side lengths to discover the perimeter.

Important Notes

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

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