(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