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MathGroup Archive 2006

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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 


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