Geometry, a branch of mathematics, defines an octagon as a closed polygon with a total of 8 sides as well as the same number of edges. When all the sides meet each other at ends forming certain angles (in a straight-line form), the shape of an octagon is formed. These line segments aren’t curved and the figure is a closed polygon. Here, let’s take a look at the formulas, properties, angles, etc. related to the same. The article will proceed to start with the basics towards the other important topics.
Understanding Octagon by referring to the examples and details
Shape: Any two-dimensional closed polygonal figure in geometry with 8 sides, 8 edges, as well as 8 angles is an octagon and this demarcates the shape from the other two-dimensional shapes or polygons like triangle, square, rectangle, pentagon, hexagon, etc.
Examples: Many different objects in our day-to-day life represent the octagonal shape. Example: * An umbrella having 8 ribs. * Sign boards marked stop at signals and roads. * Wall clock with 8 edges.
Sides: From the section above you are aware that every octagon has eight sides. The length of the sides of the respective polygon can be differentiated as regular and irregular octagons.
- The octagons with the measure of all sides and angles being equal are known as the regular octagons.
- Those octagons with unequal sides are known as irregular octagons.
Angles: Now, it is clear that the shape with 8 angles and 8 vertices is an octagon. So, it can be concluded that the octagon also has eight exterior angles as well as eight interior angles.
- Interior angles of an octagon: It should be noted that the sum of interior angles of any (regular or irregular) polygon is 1080 degrees and each interior angle of a regular octagon is (1080/8) 135 degrees.
- Exterior angles of an octagon: Exterior angles sum of an octagon is always 360 degrees and hence each exterior angle of cyclic octagon measures (360/8) 45 degrees.
It is on the basis of angels that any polygon is said to be a convex or concave shape.
- Any octagon with every angle pointing outward is a convex shape.
- On the contrary, the one with any one of the angles pointing inwards is a concave figure.
The above explanation might have cleared the picture of an octagon in your mind. Now, it would be better to move towards other topics.
Diagonals in an octagon
In any polygon of n sides, the number of diagonals=n(n-3)/2.
Hence, in an octagon, the number of diagonals will be 20.
The perimeter of the octagon
As always, the perimeter of the octagon can be obtained by adding up the length of all the sides of the octagon.
Perimeter= sum of all sides
Or perimeter= 8a (in the case of a regular octagon).
Area of an octagon
The region bounded by any figure is its area. Area of an octagon with sides=8 and each angle=135 degrees can be obtained by the formula, Area= 2a^2 (1+√2) [only for a regular octagon]
For a better understanding and application of the concept, you can subscribe to Cuemath now. This website gives a detailed description of various topics like triangle, square, rectangle, pentagon, hexagon, heptagon, nonagon, decagon, etc. Even the concepts and the explanation include the respective related topics.
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