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

```

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