(10/13/97) 

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MathMagic Cycle 25: Level 10-12 Regular 

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Using Geoboards, rubber bands and the information given below, try to build
a formula to figure out the Area (sq. units) of any polygon using only 
BOUNDARY POINTS (b) and INTERIOR POINTS (i):

+  A  *  B  +     A  *  *  B  +     +  +  +  F  +     +  +  A  +  +   
+  *  O  O  +     *  O  O  *  +     A  O  O  O  +     +  +  O  +  +   
+  D  *  *  C     B  C  O  *  +     +  B  O  O  +     F  E  O  B  C   
+  +  +  +  +     +  +  *  *  +     +  *  O  O  E     +  *  O  *  +    
+  +  +  +  +     +  +  +  D  +     +  C  *  *  D     +  +  D  +  +

Trapezoid ABCD    Polygon ABCD      Polygon ABCDEF    Polygon ABCDEF
8 boundary pts.   12 boundary pts.  9 boundary pts.   8 boundary pts.
2 interior pts.   3 interior pts.   7 interior pts.   3 interior pts.
Area= 5 sq.units  Area= 8 sq.units  Area= 10.5 sq.u.  Area= 6 sq.u.

Key: A->F: Connected boundaries; *: additional boundaries; O: interior pts;
     +: grid

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MathMagic Cycle 25: Level 10-12 Advanced 

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Working with your NTPs please find a solution for a, b, c, d, e, and f given
the following conditions:

     a(b + c + d + e + f)= 184   Hints: Try a simpler problem using say 3
     b(a + c + d + e + f)= 225          constants. Give them values. See
     c(a + b + d + e + f)= 301          what happens.
     d(a + b + c + e + f)= 369
     e(a + b + c + d + f)= 400
     f(a + b + c + d + e)= 525


Remember MathMagicians: share your thoughts with us.
            
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Good luck
MrH