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 Hexagon
- Diagonal of a Regular Heptagon
- Diagonal of a Regular Decagon
- 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
- Length of the Diagonal of the Octagon
- Find the diagonal of the Cube
- Volume of cube using its space diagonal
- Area of hexagon with given diagonal length
- Find length of Diagonal of Hexagon
- Area of a square from diagonal length
- Area of a Regular Pentagram
- Program to convert the diagonal elements of the matrix to 0
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