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

You are watching: Number of diagonals in a decagon

1.What is a Decagon?
2.Types the Decagon
3.Properties of 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 also ten angles.Thus, a decagon shape deserve to be characterized as a polygon having ten sides, ten internal angles, and also ten vertices. Based on the political parties of a decagon, they are generally classified into consistent decagons and also irregular decagons. A constant decagon has actually 35 diagonals and 8 triangles. The place of this diagonals and triangles is described in the later on sections that this article.


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

Regular and also Irregular DecagonsConvex and also Concave DecagonsSimple and complicated Decagons

Regular Decagon

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

Each internal angle in consistent decagon measures 144º, while every exterior angle steps 36º.

*

Irregular Decagon

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

*

Convex and Concave Decagons

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

*

Simple and complicated Decagons

Simple decagons refer to decagons through no political parties crossing themselves. They follow every one of the over said regular decagon rules. While facility decagons refer to decagons that space self-intersecting and have added interior spaces. They execute not strictly follow any kind of prescribed rule of decagons about their interior angles and also their sums.

*


Properties that Decagon


Some of the vital properties of decagons are listed here.

The amount of the inner angles is 1440°.The sum of the dimensions of the exterior edge is 360°.The main angle procedures 36 levels in the situation of a consistent decagon.There room 35 diagonals in a decagon.There room 8 triangle in a decagon.

Sum of the inner Angles of Decagon

To discover the amount of the inner angles the a decagon, first, division it into triangles. There are eight triangle in a continuous decagon. We recognize that the amount of the angle in each triangle is 180°. Thus,180° × 8 = 1440°. Therefore, the amount of all the internal angles the a decagon is1440°.We understand that the variety of sides of a decagon is 10. Hence, we divide the complete sum the the inner angles by 101440° ÷ 10 = 144°Thus, one inner angle the a continuous decagon shape is 144°. And, the amount of all the internal angles of a decagon is 1440°.

Measure of the main Angles that a continual Decagon

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

*

Decagon Diagonals

A diagonal line is a line that deserve to be drawn from one vertexto another. The number of diagonals of a polygon is calculated by:n(n−3) ÷ 2. In decagon, n is the number of sides i m sorry is same to 10, therefore n=10. Currently 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 involvement one vertex to the continuing to be vertices that the decagon,8 triangles will be formed. Through joiningall the vertices independently to every other, then 80 triangles (8×10) will certainly be formed. Look in ~ the image provided below, reflecting diagonals and also triangles the a decagon.

*


Decagon Formulas


Like various other shapes, a continuous decagon likewise has the formula come calculateperimeter andarea. The recipe are discussed below:

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

The formula to find the perimeter that a continuous decagon is 10 time of a next or 10 × n, whereby n is the side-length that the decagon (as all sides space equal and total sides space 10). In the case of an rarely often, rarely decagon, we can simply include the side lengths to uncover the perimeter.

Important Notes

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

See more: Yu-Gi-Oh 5Ds Akiza - 45 Akiza 5D'S Ideas

Related articles on Decagon

Check the end these interesting write-ups to know much more about decagon and also its associated topics.