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 Heptagon
- Diagonal of a Regular Pentagon
- 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 Calculate the Perimeter of a Decagon
- Area of decagon inscribed within the circle
- Find the diagonal of the Cube
- Length of the Diagonal of the Octagon
- Find length of Diagonal of Hexagon
- Area of a square from diagonal length
- Area of hexagon with given diagonal length
- Volume of cube using its space diagonal
- Calculate area of pentagon with given diagonal
- Program to convert the diagonal elements of the matrix to 0
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