How Many Diagonals are There in an Octagon and Decagon

Octagon

An octagon is a polygon with 8 sides and 8 angles in geometry. This signifies that an octagon has eight vertices and eight edges. In layman's terms, an octagon is an 8-sided polygon, often known as an 8-gon, in a two-dimensional plane. All the sides of a regular octagon are the same length. A normal octagon's internal angles are all 135°. As a result, the outside angle is calculated as 180° - 135° = 45°. The total of the octagon's inner angles is 135 x 8 = 1080°.

The octagon is a two-dimensional geometrical form. The octagon is a polygon, much like the triangle, square, pentagon, hexagon, rectangle, and other shapes we've learned in geometry. The fact that it has 8 sides, and 8 angles distinguish it from other geometrical forms.

If squares are created on all sides of an octagon, the midpoints of the sections connecting the centres of opposing squares form a quadrilateral: Equi-diagonal and ortho-diagonal ( whose diagonal lengths are equal and they bisect each other at 90 degrees).

What is The Number of Sides on an Octagon?

The octagon is an 8-sided polygon, as we well know. That is, an octagon has eight sides. Additionally, octagons are classed as regular, or irregular based on the length of their sides.

Octagonal Diagonals

The number of diagonals for each n-sided polygon may be calculated using the formula n(n - 3)/2.

Similarly, the number of diagonals in an octagon may be calculated.

n = 8 for octagon

We obtain it by substituting n = 8 in the necessary formula.

n (n – 3)/2 = 8(8 – 3)/2 = 4(5) = 20

As a result, an octagon has a total of 20 diagonals.

Decagon

A decagon is a ten-sided polygon. Polygons are two-dimensional closed forms with straight lines. Polygons are defined as triangles, squares, and decagons, but not circles or ovals.

The most fundamental decagon contains 10 equal sides and ten equal interior angles, or angles facing the inside of the polygon. Other kinds of decagons exist as well.

What is The Shape of A Decagon?

A decagon can have a variety of looks based on the category to which it belongs. Decagons are classified as follows:

· Decagons that are regular or irregular

· Decagons that are concave or convex

· Simple or complicated decagons

Diagonals of Decagon

Diagonals in a polygon are calculated using the formula n(n-3)/2, where n is the number of polygon sides.

The octagon has eight sides.

So, the number of diagonals in an Octagon is 8(8-3)/2 = 20 Ans.

A decagon has ten sides.

As a result, the number of diagonals in a decagon is 10(10-3)/2 = 35 Ans.