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What is the area of a triangle

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by logitech » Sun Dec 07, 2008 2:06 am
What is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(3, 5)?

* 3
* 4
* 5
* 6
* 7

D
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Re: What is the area of a triangle

by sudhir3127 » Sun Dec 07, 2008 2:38 am
logitech wrote:What is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(3, 5)?

* 3
* 4
* 5
* 6
* 7

D
1/2 Abs [ (x1-x2)(y2-y3) - (y1-y2)(x2-x3) ]

1/2 abs [(-4)(-4) - (2)(2) ]
1/2*12 = 6

D.
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Re: What is the area of a triangle

by logitech » Sun Dec 07, 2008 2:42 am
sudhir3127 wrote:

1/2 Abs [ (x1-x2)(y2-y3) - (y1-y2)(x2-x3) ]
Magic formula huh ? Sweat how do you derive this formula ?
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Re: What is the area of a triangle

by sudhir3127 » Sun Dec 07, 2008 3:02 am
logitech wrote:
sudhir3127 wrote:

1/2 Abs [ (x1-x2)(y2-y3) - (y1-y2)(x2-x3) ]
Magic formula huh ? Sweat how do you derive this formula ?
its one of the formulas to be learnt .. it takes into consideration matrices..
a 2X2 matrix

1/2 Absolute [ X1 - X2 X2- X3
Y1-Y2 y2-y3 ]

use 2X 2 matrix and solve the above...
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Re: What is the area of a triangle

by logitech » Sun Dec 07, 2008 10:34 am
sudhir3127 wrote:
logitech wrote:
sudhir3127 wrote:

1/2 Abs [ (x1-x2)(y2-y3) - (y1-y2)(x2-x3) ]
Magic formula huh ? Sweat how do you derive this formula ?
its one of the formulas to be learnt .. it takes into consideration matrices..
a 2X2 matrix

1/2 Absolute [ X1 - X2 X2- X3
Y1-Y2 y2-y3 ]

use 2X 2 matrix and solve the above...
Good old determinant :)

x1 y1 1
x2 y2 1
x3 y3 1

Cool.
LGTCH
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sol

by vivek.kapoor83 » Sun Dec 07, 2008 10:55 am
logitech,
it took me less than 2mins to solve it but 28 mins to draw this........ :P
im attaching the solution
Image
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by logitech » Sun Dec 07, 2008 11:06 am
SWEET!!
LGTCH
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Re: What is the area of a triangle

by srisl11 » Sun Dec 07, 2008 11:08 am
sudhir3127 wrote:
logitech wrote:
sudhir3127 wrote:

1/2 Abs [ (x1-x2)(y2-y3) - (y1-y2)(x2-x3) ]
Magic formula huh ? Sweat how do you derive this formula ?
its one of the formulas to be learnt .. it takes into consideration matrices..
a 2X2 matrix

1/2 Absolute [ X1 - X2 X2- X3
Y1-Y2 y2-y3 ]

use 2X 2 matrix and solve the above...
Very handy formula...
Thank you Sudhir
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by Tryingmybest » Sun Dec 07, 2008 12:14 pm
Logitech . check if this works

Area of triangle =sqrt {s(s-a)(s-b)(s-c) }

where s=(a+b+c)/2
a,b,c are sides of triangle.

From given data find the sides and substitute in the formula
we get area 6.
This is handy when coordinates are not given but length of the sides are given.
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by logitech » Sun Dec 07, 2008 12:28 pm
Thanks guys. I solved this question as vivek.kapoor83. But I liked the determinants method.
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by vishubn » Sun Dec 07, 2008 6:35 pm
its one of the formulas to be learnt .. it takes into consideration matrices..
a 2X2 matrix

1/2 Absolute [ X1 - X2 X2- X3
Y1-Y2 y2-y3 ]

use 2X 2 matrix and solve the above...
Hi SUdhir !

If u dont mind can u elaborate more on this ! i mean its a nice method ! :) but still not able to get the thought process !!

vishu
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by logitech » Sun Dec 07, 2008 6:59 pm
vishubn wrote:
its one of the formulas to be learnt .. it takes into consideration matrices..
a 2X2 matrix

1/2 Absolute [ X1 - X2 X2- X3
Y1-Y2 y2-y3 ]

use 2X 2 matrix and solve the above...
Hi SUdhir !

If u dont mind can u elaborate more on this ! i mean its a nice method ! :) but still not able to get the thought process !!

vishu
Okay...Are you ready ? :o

https://people.richland.edu/james/lectur ... /area.html

Have fun!
LGTCH
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by hwiya320 » Sun Dec 07, 2008 7:07 pm
I actually use the same method to draw a rectangle around it to solve it. I found this out when I was solving one of the Kaplan problem that it was easier for me to picture that.

good job with the drawing!
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by vishubn » Sun Dec 07, 2008 7:42 pm
Okay...Are you ready ? Surprised

https://people.richland.edu/james/lectur ... /area.html

Have fun!

Thanks Logitech !! indeed nice approach


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by GMATinsight » Fri Sep 30, 2016 7:03 pm
logitech wrote:What is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(3, 5)?

* 3
* 4
* 5
* 6
* 7

D
Please find the solution as attached
Attachments
Solution GMATinsight.jpg
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