Given an integer a which is the side of a regular decagon, the task is to find and print the length of its diagonal.
Input: a = 5
Input: a = 9
Approach: We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the no. of sides in the polygon.
So, sum of interior angles of decagon = 8 * 180 = 1440 and each interior angle will be 144.
Now, we have to find BC = 2 * x. If we draw a perpendicular AO on BC, we will see that the perpendicular bisects BC in BO and OC, as triangles AOB and AOC are congruent to each other.
So, in triangle AOB, sin(72) = x / a i.e. x = 0.951 * a
Therefore, diagonal length will be 2 * x i.e. 1.902 * a.
Below is the implementation of the above approach:
- Diagonal of a Regular Pentagon
- Diagonal of a Regular Hexagon
- Diagonal of a Regular Heptagon
- Length of Diagonal of a n-sided regular polygon
- Filling diagonal to make the sum of every row, column and diagonal equal of 3x3 matrix
- Area of decagon inscribed within the circle
- Program to Calculate the Perimeter of a Decagon
- Length of the Diagonal of the Octagon
- Find the diagonal of the Cube
- Volume of cube using its space diagonal
- Find length of Diagonal of Hexagon
- Area of hexagon with given diagonal length
- Area of a square from diagonal length
- Calculate area of pentagon with given diagonal
- Area of a Regular Pentagram
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.