(10/13/97) (Reminder to *REGISTERED* teams: You can now work with Net Team Partners (NTPs) that are not registered, just subscribed to the "mathmagic-10-12- open" list. Feel free to advertize your team name, location and e-mail, along with the geographical location of the desired partner. To do so, just send an e-mail to mathmagic-10-12@mathforum.org. PLEASE remember this only works if you have paid and been included in one of the WELCOMES regularly posted.) *************************************** 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 * 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 **************************************** 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 + 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. ============================ Good luck MrH