Re: find area bounded by three linear functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg68387] Re: find area bounded by three linear functions*From*: "Ray Koopman" <koopman at sfu.ca>*Date*: Thu, 3 Aug 2006 06:07:19 -0400 (EDT)*References*: <eaprqf$s4d$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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 In[1]:= 1/2 Abs@Det[ Flatten[{x,y,1}/.Solve[#,{x,y}]]& /@ Subsets[{x == 3y, x + y == 0, 7x + 3y == 24}, {2}] ] Out[1]= 12