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Need HELP with the 6th grade math pow.

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Triangle Area


Above is a set of dots in a 5 by 5 array.  You can make a triangle by connecting any three of these dots.  How many triangles can you make that have an area equal to the triangle to the left? The distance vertically and horizontally is one unit (do not use inches or cm).  A triangle in a different location is considered a different triangle.



Organize by Triangle type:

1. the original triangle, just moved
2. triangles with a base of 1
3. triangles with a base of 3
4.  Cut the original triangle in half (cutting the smallest side in half).  Imagine a hinge on this half of the small side that can flip half of the triangle around so that it creates a very long skinny triangle.  Find all of these triangles.


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Do you see that the area of the isosceles triangle is 3/2?  Using the pythagorean theorem, you can find that the base has length sqrt(2) and the 2 legs have length sqrt(5), which makes the height = 3*sqrt(2)/2.  So triangles with base=3 and height=1 will have area=3/2.  So will triangles with base=1 and height=3.  The triangle described in option 4 has base=3*sqrt(2) and height=sqrt(2)/2.  


Where did you find this problem?  

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