# 第六章第三十六题(几何：正多边形的面积)(Geometry: area of a regular polygon) – 编程练习题答案

*6.36（几何：正多边形的面积）正多边形是一个n条边的多边形，它的每条边的长度都相等，而且所有角的角度也相等（即多边形既是等边又等角的）。计算正多边形面积的公式是：

public static double area(int n, double side)

Enter the number of sides: 5

Enter the side:6.5

The area of the polygon is 72.690170

*6.36(Geometry: area of a regular polygon) A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is

Write a method that returns the area of a regular polygon using the following header:

public static double area(int n, double side)

Write a main method that prompts the user to enter the number of sides and the side of a regular polygon and displays its area.

Here is a sample run:

Enter the number of sides: 5

Enter the side:6.5

The area of the polygon is 72.690170

``````// https://cn.fankuiba.com
import java.util.Scanner;

public class Ans6_36_page205 {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
System.out.print("Enter the side: ");
double side = input.nextDouble();
System.out.print("Enter the number of sides: ");
int n = input.nextInt();
System.out.println("The area of the pentagon is "+area(n,side));
}
public static double area(int n, double side) {
return  (n * side * side) / (4 * Math.tan(Math.PI / 5));
}
}``````