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September 4th, 2012, 08:42 PM   #1
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Area of triangle ABC

[attachment=0:y2tsqyu1]Area of triangle ABC.JPG[/attachment:y2tsqyu1]
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September 4th, 2012, 10:23 PM   #2
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Re: Area of triangle ABC

Using coordinate geometry:

Orient the coordinate axes such that D is the origin. Then we have A(-3,3), B(0,5) and C(5,0), and the area A of the triangle ABC is then:

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September 5th, 2012, 04:19 PM   #3
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AD and BC are parallel, so area of triangle ABC = area of triangle DBC = 25/2.
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September 5th, 2012, 05:40 PM   #4
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Re: Area of triangle ABC

Total area (including triangle ABH) = 25 + 9 + 3 = 37
"White area" = 5*5/2 + 3*8/2 = 24.5
"Yellow area" = 37 - 24.5 = 12.5
How come such an easy one, Albert; feeling guilty?
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September 5th, 2012, 06:17 PM   #5
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Re: Area of triangle ABC

Here is a vectored approach. BD+DC=BC. BH+HA=BA. Then the area is 1/2*|BA x BC|. You can do it from any of the points of the triangle and with different choices of direction.
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September 5th, 2012, 07:09 PM   #6
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Re: Area of triangle ABC

Hello, Albert.Teng!

Quote:


Code:
                B               G
                * - - - - - - - - *
              * | *               |
            *   |   *             |
          *     |     *           |
        *       |       *         | 5
    A * - - - - *         *       |
      |      *  |           *     |
    3 |         |   *         *   |
      |         |          *    * |
      * - - - - * - - - - - - - - *
      F    3    D        5        C










[color=beige]. . . . . . . . . . . [/color]

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September 5th, 2012, 07:18 PM   #7
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Re: Area of triangle ABC

Quote:
Denis wrote :How come such an easy one, Albert; feeling guilty?
I have posted so many tough problems, as you said may be a little bit

guilty.

Do you like easy ones or questions with challenging?
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September 5th, 2012, 08:29 PM   #8
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Re: Area of triangle ABC

NO easy ones please!
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September 6th, 2012, 01:49 AM   #9
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Re: Area of triangle ABC

[color=#000000]Another solution (similar to soroban's).[/color]





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September 6th, 2012, 04:00 AM   #10
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Re: Area of triangle ABC

Quote:
Originally Posted by Albert.Teng
[attachment=0:1flowknc]Area of triangle ABC.JPG[/attachment:1flowknc]
Heres a hard way to do this easy problem...

By pythagoras,

By heron,



I like skipjack approach, he slides point A to point D along AD and yellow area never changes.

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