十二面体表面积程序

给定十二面体的边缘，计算其表面积。表面积是形状的所有面占据的空间量。
公式： $\mathbf{A=3\sqrt{25+10\sqrt{5}}\hspace{2 mm} a^{2}}$
例子：

Input : 3
Output : 185.812

Input : 7
Output : 1011.64

十二面体是由 12 个面或平面组成的 3 维图形。所有的面都是相同大小的五边形。 “十二面体”这个词来自希腊语dodeca（“十二”）和hedron（“面”）。每个形状都有属性和特征。十二面体也是如此

• 12个相等的五边形面
• 20 个顶点
• 30 条边

其中五边形是具有 5 个直边和 5 个顶点的二维形状。因此，一个十二面体有 12 个这些平坦、相等的五边形面。因此，可以将十二面体视为 12 面骰子（通常看不到），但可以在 Battleball 棋盘游戏中。

C++

// CPP program to calculate
// surface area of dodecahedron
#include 
using namespace std;
 
// utility Function
double area_of_dodecahedron(int side)
{
    return ((3 * sqrt(25 + 10 * (sqrt(5))))
                        * (pow(side, 2))) ;
}
 
// Driver Function
int main()
{
    int side = 3;
     
    cout<< "Surface area of dodecahedron = "
            << area_of_dodecahedron(side);
         
        return 0;
}

Java

//Java program to calculate
// surface area of dodecahedron
 
class GFG
{
 
    // Utility Function
    static double area_of_dodecahedron(int side)
    {
        return ((3 * Math.sqrt(25 + 10 * (Math.sqrt(5))))
                        * (Math.pow(side, 2))) ;
    }
     
    // Driver Function
    public static void main (String[] args)
    {
        int side = 3;
        System.out.println("Surface area of dodecahedron ="
                              + area_of_dodecahedron(side));
    }
 
}
 
// This code is contributed by Azkia Anam.

Python3

# Python program to calculate
# surface area of dodecahedron
import math
 
# utility Function
def area_of_dodecahedron(side):
 
    return ((3 * math.sqrt(25 + 10 * (math.sqrt(5))))* (math.pow(side, 2)))
 
# Driver Function
side = 3
print("Surface area of dodecahedron = ",
      round(area_of_dodecahedron(side), 3))
 
# This code is contributed
# by Azkia Anam.

C#

//C# program to calculate
// surface area of dodecahedron
using System;
 
class GFG
{
 
    // Utility Function
    static float area_of_dodecahedron(int side)
    {
        return (float)((3 * Math.Sqrt(25 + 10 * (Math.Sqrt(5))))
                        * (Math.Pow(side, 2))) ;
    }
     
    // Driver Function
    public static void Main ()
    {
        int side = 3;
        Console.WriteLine("Surface area of dodecahedron ="
                            + area_of_dodecahedron(side));
    }
 
}
 
// This code is contributed by vt_m.

Javascript

 
// Javascript program to calculate
// surface area of dodecahedron
 
// utility Function
function area_of_dodecahedron( side)
{
    return ((3 * Math.sqrt(25 + 10 * (Math.sqrt(5))))
                        * (Math.pow(side, 2))) ;
}
 
 
    // Driver Code
     
    let side = 3;
     
    document.write("Surface area of dodecahedron = "
    + Math.round(area_of_dodecahedron(side)*1000)/1000);
     
     

输出：

Surface area of dodecahedron = 185.812