Question 1197252
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find the {{{highlight(cross(are))}}} <U>area</U> of a quadrilateral having points (5,2), (4,3), (2,4), (-8,-1) as consecutive vertices.
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Place your quadrilateral, whose vertices are the lattice points, into the minimal rectangle,

whose boundary lines are parallel to x- and y-axis.


Find the area of this rectangle as the product of its dimensions.


From this area, subtract the areas of all triangles and rectangles (squares) that are inside the rectangle
but outside the quadrilateral.


Calculating these areas is easy: it requires multiplication of integer numbers, only
(sometimes, dividing by 2 is needed).


Doing this way, every 4-th grade student can complete such job on his or her own.



Another way is to plot vertices to make sure that the quadrilateral is convex;

then to draw a diagonal and to calculate the areas of two triangles using the Heron's formula;

finally to add the areas of the triangles.



Third way is to use the "shoelace formula".

On the "shoelace formula" to calculate the area of a polygon see these sources

https://en.wikipedia.org/wiki/Shoelace_formula

https://www.101computing.net/the-shoelace-algorithm/

https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem

https://www.tuitionkenneth.com/a-maths-area-shoelace-method