# Re: Triangle Area (#160)

**URL:** <https://www.ruby-forum.com/t/re-triangle-area-160/135646>\
**Category:** Ruby\
**Created:** [April 23, 2008, 9:15pm UTC](https://www.ruby-forum.com/t/re-triangle-area-160/135646 "2008-04-23T21:15:39Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![jameskelly](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/j/3ab097/32.png) [@jameskelly](https://www.ruby-forum.com/u/jameskelly)\
**Post date:** [April 23, 2008, 9:15pm UTC](https://www.ruby-forum.com/t/re-triangle-area-160/135646/1 "2008-04-23T21:15:39Z")

</div>

Thanks for your work in keeping up RubyQuiz! My spare thinking time has  
been taken up by other work lately, but this one’s simple enough that I  
feel fairly confident in typing up this solution while away from the  
nearest computer with a Ruby interpreter installed (browser Ruby didn’t  
work for testing).

As a competition-loving math student, for me the obvious way to  
calculate the area of a triangle is Hero’s formula:

class Vector  
def distance(oth)  
Math.sqrt(to\_a.zip(oth.to\_a).inject(0){|s,(a,b)|s+(a-b)\*\*2})  
end  
end

class Triangle  
def area  
ab = @a.distance(@b)  
bc = @b.distance(@c)  
ac = @a.distance(@c)  
s = (ab+bc+ac)/2  
Math.sqrt(s\*(s-ab)_(s-bc)_(s-ac))  
end  
end

----- Original Message ----  
From: Matthew M. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid)  
To: ruby-talk ML [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid)  
Sent: Saturday, April 19, 2008 11:39:34 AM  
Subject: [QUIZ] Triangle Area (#160)

Apologies for the latest… Some busy stuff this week in “real life.”  
In light of that, I’ve kept this quiz simple: you only need implement  
one function. I do provide brief descriptions of a few possible  
techniques, but don’t feel you need to do them all! Just pick one that  
sounds interesting to you…

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Quiz #160  
Triangle Area

Start with the following code for a Triangle class:

```
require 'matrix'

RANDOM_PT = lambda { Vector[rand(101)-50, rand(101)-50] }

class Triangle
    def initialize(a, b, c)
        @a, @b, @c = a, b, c
    end

    def Triangle.random(foo = RANDOM_PT)
        Triangle.new(foo.call, foo.call, foo.call)
    end

    def [](i)
        [@a, @b, @c][i]
    end

    def area
        # Fill in this stub.
    end

    def inspect
        "Triangle[#{@a}, #{@b}, #{@c}]"
    end
    alias to_s inspect
end

```

Your task this week is to write the code for the `area` method.

There are a few techniques that come to mind for determining (or  
closely  
estimating) the area of a triangle. You do not need to attempt all of  
these;  
just pick a technique that sounds fun and do implement it.

1. Determinant Method

It is possible to calculate the area of a triangle very simply using  
just the  
points as part of a matrix, and calculating the determinant of that  
matrix.  
See ([Classroom Resources - National Council of Teachers of Mathematics](http://mathforum.org/library/drmath/view/55063.html)) for an  
explanation  
of the technique. This is quick and easy, so if you don’t have much  
time this  
week, try this.

1. Monte Carlo Method

The Monte Carlo method first requires that you determine a bounding  
area  
(typically a box) that surrounds the test area (i.e. the triangle).  
Then you  
choose thousands of random points within the box, determining for each  
point  
whether it falls inside or outside the triangle.

Knowing the area of the box (an easier calculation) and the percentage  
of  
random points that fell inside the triangle, you can multiply those  
two values  
together to get the triangle’s area.

1. Scan-Line Method

Imagine covering the triangle with horizontal bars of a certain  
height, such  
that each bar is only wide enough to hide the triangle underneath.  
Knowing  
the width and height of each bar (i.e. rectangle) lets you calculate  
the area  
of each, and summed together is an approximation of the triangle’s  
area.

(This is sometimes called a scan-line method, as you are examining  
horizontal  
slices of the subject, very much like a television scan line draws a  
number of  
horizontal slices of the picture.)

Each time the height of the bars are halved (and twice as many are  
employed),  
your estimate of the triangle’s area will improve. Those familiar with  
calculus  
will recognize this as integration, as the height of each horizontal  
slice  
approaches zero.

1. Something else!

If none of these methods interest you, but you have with another  
method to  
estimate or determine exactly the triangle’s area, please do!

```
  ____________________________________________________________________________________

```

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