计算给定对角线的五边形面积

原文:https://www . geeksforgeeks . org/计算给定对角线的五边形面积/

给定一个整数 d ，它是一个五边形的对角线长度，任务是找到那个五边形的面积。

pentagon

例:

输入: d = 5 输出: 16.4291 输入: d = 10 输出: 65.7164

逼近:五边形是一个正多边形，有五条等边，所有的角都相等。五边形的内角各为 108 度，五边形所有角度之和为 540 度。如果 d 是五边形的对角线，那么它的面积由下式给出:

$ \frac{1}{8} {d^2 (-5+ \sqrt{45})\sqrt{ \sqrt{20} + 5 } } $

以下是上述方法的实现:

C++

// C++ program to find the area of
// Pentagon with given diagonal
#include <bits/stdc++.h>
using namespace std;

// Function to return the area of the
// pentagon with diagonal d
float pentagonArea(float d)
{
    float area;

    // Formula to find area
    area = (d * d * (-5 + sqrt(45)) * sqrt(sqrt(20) + 5)) / 8;

    return area;
}

// Driver code
int main()
{
    float d = 5;
    cout << pentagonArea(d);
    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to find the area of
// Pentagon with given diagonal
import java.text.*;
class GFG{
// Function to return the area of the
// pentagon with diagonal d
static double pentagonArea(double d)
{
    double area;

    // Formula to find area
    area = (d * d * (-5 + Math.sqrt(45)) * Math.sqrt(Math.sqrt(20) + 5)) / 8;

    return area;
}

// Driver code
public static void main(String[] args)
{
    double d = 5;
    DecimalFormat dec = new DecimalFormat("#0.0000");
    System.out.println(dec.format(pentagonArea(d)));
}
}
// This code is contributed by mits

Python 3

# Python3 program to find the area of
# Pentagon with given diagonal

# from math lib import sqrt() method
from math import sqrt

# Function to return the area of the
# pentagon with diagonal d
def pentagonArea(d) :

    # Formula to find area
    area = (d * d * (-5 + sqrt(45)) * sqrt(sqrt(20) + 5)) / 8

    return round(area , 4)

# Driver code
if __name__ == "__main__" :

    d = 5
    print(pentagonArea(d))

# This code is contributed by Ryuga

C

// C# program to find the area of
// Pentagon with given diagonal
using System;

class GFG{
// Function to return the area of the
// pentagon with diagonal d
static double pentagonArea(double d)
{
    double area;

    // Formula to find area
    area = (d * d * (-5 + Math.Sqrt(45)) * Math.Sqrt(Math.Sqrt(20) + 5)) / 8;

    return area;
}

// Driver code
public static void Main()
{
    double d = 5;
    Console.WriteLine("{0:F4}",pentagonArea(d));
}
}
// This code is contributed by mits

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP program to find the area of
// Pentagon with given diagonal
// Function to return the area of the
// pentagon with diagonal d
 Function pentagonArea($d)
{
    $area;

    // Formula to find area
    $area= ($d * $d * (-5 +sqrt(45)) * sqrt(sqrt(20) + 5)) / 8;

    return $area;
}

// Driver code
{
    $d = 5;
    echo(pentagonArea($d));
    return 0;
}
//This code is contributed by Mukul singh.

java 描述语言

<script>
// javascript program to find the area of
// Pentagon with given diagonal

// Function to return the area of the
// pentagon with diagonal d
function pentagonArea( d)
{
    let area;

    // Formula to find area
    area = (d * d * (-5 + Math.sqrt(45)) * Math.sqrt(Math.sqrt(20) + 5)) / 8;
    return area;
}

// Driver code
    let d = 5;
    document.write(pentagonArea(d).toFixed(4));

// This code is contributed by gauravrajput1
</script>

Output: 

16.4291

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