Puzzle | convex quadrilateral

 
 
Find a convex quadrilateral such that the quadrilateral has the smallest area and all four of its sides (a, b, c, d),   two diagonals (e, f) and area K are :

(1)   distinct integers
(2)   distinct prime integers

 

In a convex quadrilateral, the two diagonals cut the interior into four triangles, each with integer area.

What do you notice about the product of these areas?

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

7 Responses to Puzzle | convex quadrilateral

  1. paul says:

    This might be the one for part a

    {a, b, c, d} = {52,25,39,60}
    {e, f} = {63, 56}
    area = 1764 sqr units

    Here is a link to a diagram

    Paul

  2. paul says:

    but one of the diagonals isn’t integer, its 36.5 in that arrangement.:)
    P.

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