1)How to find the area bounded by the 4 points in a coordinate?

Question

2)what is the formula?
3)how the formula related to that?

Answer 1

The area can be found by using cross multiplication of elements in a rectangular matrix formed by the coordinates of the 4 (or any number) points.

Let P be a 5x2 matrix, where the columns represnt the x and y coordinates.

Rows 1 to 4 represent the (x,y) ordered pairs of the 4 points, and the fifth row is a repetition of the fist row.

The area is obtained by the following formula:

Area=|(ΣP(i,1)*P(i+1,2)-P(i+1,1)*P(i,2))|/2 for i=1 to 4.

Example:
Find area of
(1,2)
(2,4)
(1,4)
(5,5)

Repeat the first row:
(1,2)
(2,4)
(1,4)
(5,5)
(1,2)
Form sum
Area=|(1*4-2*2+2*4-1*4+1*5-5*4+5*2-1*5)|/2
=3