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:
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- 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
- Program to Calculate the Perimeter of a Decagon
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- Find length of Diagonal of Hexagon
- Area of a square from diagonal length
- Area of hexagon with given diagonal length
- Calculate area of pentagon with given diagonal
- Volume of cube using its space diagonal
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