Re: find area bounded by three linear functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg68386] Re: [mg68357] find area bounded by three linear functions*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 3 Aug 2006 06:07:16 -0400 (EDT)*References*: <200608020924.FAA28580@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 2 Aug 2006, at 11:24, T Harris wrote: > 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 > First, find the coordinates of the points of intersections of the lines: In[1]:= pts = {x, y} /. Solve /@ Subsets[{x == 3*y, x + y == 0, 7*x + 3*y == 24}, {2}] Out[1]= {{{0, 0}}, {{3, 1}}, {{6, -6}}} Next, compute the lengths of the sides of the triangle: In[2]:= {a, b, c} = Norm /@ Apply[Subtract, Subsets[pts, {2}], {1}] Out[2]= {Sqrt[10], 6*Sqrt[2], Sqrt[58]} Now use Heron's formula: In[3]:= s=Total[{a,b,c}]/2; In[4]:= Sqrt[s*(s-a)*(s-b)*(s-c)]//N Out[4]= 12. Andrzej Kozlowski

**References**:**find area bounded by three linear functions***From:*"T Harris" <tdh1967@bellsouth.net>