Java Problem - How to find area of a polygon if number of sides and coordinates are given

Lets write a program to find the area of a polygon if number of sides and coordinates are given.

Program Structure

Here follows the program structure

• The first line reads the number of sides of the polygon.
• The second line reads the each coordinates reads in x1 y1 x2 y2 x3 y3.....xn yn format.
• the next line prints the output, which is the total area of a polygon.

Example

Inputs are

4
0 0 0 4 4 4 4 0

Output is

16.00

Solution

The mathematical formula for finding total area of a polygon is

 | 1/2 [ (x1y2 + x2y3 + ... + xn-1yn + xny1) -  (x2y1 + x3y2 + ... + xnyn-1 + x1yn) ] ||

Program

Here follows the java program for finding the total area of a polygon by applying above formula