Given an integer a which is the side of a regular pentagon, the task is to find and print the length of its diagonal.
Input: a = 6
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 pentagon = 3 * 180 = 540 and each interior angle will be 108.
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(54) = x / a i.e. x = 0.61 * a
Therefore, diagonal length will be 2 * x i.e. 1.22 * a.
Below is the implementation of the above approach:
- Calculate area of pentagon with given diagonal
- Diagonal of a Regular Decagon
- Diagonal of a Regular Heptagon
- Diagonal of a Regular Hexagon
- 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
- Program to find the Area of Pentagon
- Find the diagonal of the Cube
- Length of the Diagonal of the Octagon
- Find length of Diagonal of Hexagon
- Area of hexagon with given diagonal length
- Area of a square from diagonal length
- Volume of cube using its space diagonal
- Program to convert the diagonal elements of the matrix to 0
- 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.