Area Of Polygon In Coordinate Geometry

Polygon can be defined as packed or closed shape made by joining more than two line segments end to end. The sides of a Polygon never bisect each other. The Point where two lines meet is known as vertex of polygon.
Now we will see how to find the Area of Polygon in coordinate Geometry?
For finding the area of polygon we have to follow some steps which are given below:
Step 1: First we take two axis in a plane which is named as ‘x’ and y- axis.
Step 2: Then we draw a polygon on the plane.
Step 3: Then we find the coordinates of given polygon.
Step 4: If we have all the coordinates of a polygon then we can easily find the area of polygon by putting all the coordinates in formula shown below.
The formula for finding the area of polygon by using the coordinates: 

Now we see how to find the area of polygon by using the above steps:
A polygon is given then we can find the area of polygon by putting the values in the formula:

 
So we can write it as:
     X  Y
P  5  9
Q  8  7
R  10 3
S   3  3
P   5  9
 
Multiply 5 by 9, we get 45 and multiply 8 by 9 we get 72;
5 * 9 = 45;
8 * 9 = 72;
So we can write it as:
45 – 72 = -27;
When we multiply 8 by 3 we get 24 and multiply 10 by 7 we get 70;
8 * 3 = 24;
10 * 7 = 70;
So we can write it as:
24 – 70 = -46;
When we multiply 10 by 3 we get 30 and multiply 3 by 3 we get 9;
10 * 3 = 30;
3 * 3 = 9;
So we can write it as:
30 – 9 = 21;
When we multiply 3 by 9 we get 27 and multiply 5 by 3 we get 15;
3 * 9 = 27;
5 * 3 = 15;
So we can write it as:
27 – 15 = 12;
Now add all the value and then divide the number by 2 we get the area of polygon.
So the sum of all the values is:
=> -27 – 46 + 21 + 12;
=> -73 + 33;
=> -40;
Then the area of polygon is:
A = | -40/ 2|
A = 20 inch²