Question
1)How to find the area bounded by the 4 points in a coordinate?
2)what is the formula?
3)how the formula related to that?
2)what is the formula?
3)how the formula related to that?
Answers
MathMate
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
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