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

```

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