Question 1149554
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1.  Make a sketch (making sketch is a <U>necessary</U> part of the solution to this problem (!) ).



2.  Conclude your figure into the smallest possible rectangle with horizontal and vertical sides.

    This rectangle has dimensions 10 (=4-(-6)) units horizontally and 8 (=8-0) units vertically, so its area is 80 square units.



3.  Cut (mentally) 4 right angled triangles from this large rectangle to get the smaller rectangle.

    The legs of these triangles are  2 and 4  units  and  8 and 4  units.



4.  So, from the area of the large rectangle you should subtract  the areas of these 4 triangles


         80 - {{{2*(1/2)*2*4}}} - {{{2*(1/2)*8*4}}} = 80 - 8 - 32 = 40.


Thus you get  the <U>ANSWER</U>  40 square units for the area of your rectangle

without using the distance formula and without calculating radicals.
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This <U>simple</U> method often works for more complicated cases of arbitrary polygons, 

if the vertices of a polygon lie in integer points of the coordinate grid.


Using this approach, even 3-th or 4-th grade student is able to solve similar problems, even although he (or she)

doesn't know yet the distance formula and radicals.