(10/13/97)
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***************************************
MathMagic Cycle 25: Level 10-12 Regular
***************************************
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
*
D
+
+
*
O
*
+
+
B
O
*
+
+
+
+
C
+
+
A
*
B
+
+
Trapezoid ABCD
8 boundary pts.
2 interior pts.
Area= 5 sq.units
*
O
C
+
+
*
O
O
*
+
B
*
*
*
D
+
+
+
+
+
+
A
+
+
+
Polygon ABCD
12 boundary pts.
3 interior pts.
Area= 8 sq.units
+
O
B
*
C
+
O
O
O
*
F
O
O
O
*
+
+
+
E
D
Polygon ABCDEF
9 boundary pts.
7 interior pts.
Area= 10.5 sq.u.
+
+
F
+
+
+
+
E
*
+
A
O
O
O
D
+
+
B
*
+
+
+
C
+
+
Polygon ABCDEF
8 boundary pts.
3 interior pts.
Area= 6 sq.u.
Key: A->F: Connected boundaries; *: additional boundaries; O: interior
pts;
+: grid
****************************************
MathMagic Cycle 25: Level 10-12 Advanced
****************************************
Working with your NTPs please find a solution for a, b, c, d, e, and f
given
the following conditions:
a(b
b(a
c(a
d(a
e(a
f(a
+
+
+
+
+
+
c
c
b
b
b
b
+
+
+
+
+
+
d
d
d
c
c
c
+
+
+
+
+
+
e
e
e
e
d
d
+
+
+
+
+
+
f)=
f)=
f)=
f)=
f)=
e)=
184
225
301
369
400
525
Hints: Try a simpler problem using say 3
constants. Give them values. See
what happens.
Remember MathMagicians: share your thoughts with us.
============================
Good luck
MrH