RE: find area bounded by three linear functions
- To: mathgroup at smc.vnet.net
- Subject: [mg68389] RE: [mg68357] find area bounded by three linear functions
- From: "Erickson Paul-CPTP18" <Paul.Erickson at Motorola.com>
- Date: Thu, 3 Aug 2006 06:07:21 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hopefully someone has some modula with this in it, but ... In[42]:= (* define Heron's formula *) triangularArea[ a_, b_, c_] := Sqrt[(a + b + c)(a + b - c)(b + c - a)(c + a - b)]/ 4 In[43]:= (* enter line equations *) eqs = {x == 3y, x + y == 0, 7x + 3y == 24} Out[43]= {x == 3 y, x + y == 0, 7 x + 3 y == 24} In[44]:= (* determine vertices by solving paired equations *) vertexs = Map[ Flatten, Union[ Map[ Solve, Sort[ Map[ Most, Permutations[ eqs] , 1] ], 1 ] ] ] Out[44]= {{x -> 0, y -> 0}, {x -> 3, y -> 1}, {x -> 6, y -> -6}} In[45]:= (* find distances by delta vertices, eliminate negative with take 3 or sort and sqrt or sum of sqr *) { a, b, c } = Map[ (#[[1]]^2 + #[[2]]^2)^(1/2) &, Take[ Sort[ Map[ #[[1]] - #[[2]] &, Union[ Map[ Most, Permutations[ Map[ { x, y} /. # & , vertexs, 1 ] ] , 1 ] ] , 1 ] ] , 3 ] , 1] Out[45]= \!\({6\ \@2, \@10, \@58}\) In[46]:= (* apply distances to Heron's formula *) N[ triangularArea[ a, b, c ] ] Out[46]= 12. -----Original Message----- From: T Harris [mailto:tdh1967 at bellsouth.net] To: mathgroup at smc.vnet.net Subject: [mg68389] [mg68357] find area bounded by three linear functions How can I get Mathematica to find the area of the region bounded by all three of the following linear functions? I have tried searching and can't find it. What do I search for to find the commands to accomplish this? I calculated by hand and come up with about 3.1623 sq. units for area above the x-axis and 8.8378 sq. units below it. The total area for the scalene triangle formed is 12 square units by my calculations using Heron's formula. X=3Y; X+Y=0; 7X + 3Y =24 Thanks, T Harris