geometry

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?

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  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

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    posted by MathMate

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