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Area of the triangle

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Area of the triangle

by gmattesttaker2 » Sun Oct 13, 2013 6:08 pm
Hello,

I was wondering if you can please assist with the following question:

A triangle in the xy-coordinate plane has vertices with coordinates (7, 0), (0, 8), and (20, 10). What is the area of this triangle?

OA: 87

Sorry if my question is trivial but I was just wondering why I cannot calculate the area of the triangle here as 1/2 x sq. root 269 x sq. root 113 ? Thanks for your help - Sri
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by Brent@GMATPrepNow » Sun Oct 13, 2013 6:14 pm
Hi Sri,

You are assuming that this is a right triangle. Are you sure it is?


There's another approach you haven't considered.
Hint: Try drawing a rectangle around the triangle.
Another hint here: https://www.beatthegmat.com/coordinate-p ... 63268.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by theCodeToGMAT » Sun Oct 13, 2013 9:03 pm
Area of Trapezium - Area of Triangle 1 - Area of Triangle 2
= 1/2 (20) (8+10)) - 1/2 (7)(8) - 1/2 (13)(10)
= 180 - 28 - 65
= 87
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by Faheem.Mustafa » Sun Oct 13, 2013 9:29 pm
gmattesttaker2 wrote:Hello,

I was wondering if you can please assist with the following question:

A triangle in the xy-coordinate plane has vertices with coordinates (7, 0), (0, 8), and (20, 10). What is the area of this triangle?

OA: 87

Sorry if my question is trivial but I was just wondering why I cannot calculate the area of the triangle here as 1/2 x sq. root 269 x sq. root 113 ? Thanks for your help - Sri
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by lunarpower » Mon Oct 14, 2013 3:02 am
Hey, I wrote this problem!

If I were 11 years old, I would just draw a 20 x 10 rectangle around everything. Then I could subtract out the three areas I don't want, which, conveniently enough, are all right triangles.
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by lunarpower » Mon Oct 14, 2013 3:05 am
To the original poster:
gmattesttaker2 wrote:Sorry if my question is trivial but I was just wondering why I cannot calculate the area of the triangle here as 1/2 x sq. root 269 x sq. root 113 ? Thanks for your help - Sri
Ironically, the answer to this question is in the diagram that you provided yourself.

Take a look at the "rise" and "run" values that you put in your own diagram. The slope of the left-hand leg is -8/7; the slope of the right-hand leg is 10/13.
These aren't perpendicular. (The slope perpendicular to -8/7 is 7/8; the slope perpendicular to 10/13 is -13/10.)
Ron has been teaching various standardized tests for 20 years.

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