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GMAT Coordinate Geometry http://www.800score.com/forum/viewtopic.php?f=3&t=9 
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Author:  questioner [ Tue Jun 08, 2010 3:57 pm ] 
Post subject:  GMAT Coordinate Geometry 
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,2), (2, 6), (15, 2), (15,4)? A. 91 B. 95 C. 104 D. 117 E. 182 (A) First, we should make a rough sketch of the figure to determine its general shape. Its left side and right side are parallel, with the left side having a length of 8 and the right side having a length of 6. The distance between these two sides is 13.This figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is: Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides. We can now determine the area of the quadrilateral: Area = 1/2 × (8 + 6) × 13 = 1/2 × 14 × 13 = 7 × 13 = 91. The correct answer is choice (A). Alternate Method (Breaking the figure apart): Without the formula for the area of a trapezoid, we can still solve the problem. We can draw two horizontal lines through the figure, one at y = 2 and one at y = 2 to divide the trapezoid into an upper triangle, a rectangle, and a lower triangle. The upper triangle has an area of (1/2) × 4 × 13 = 26. The rectangle has an area of 4 × 13 = 52. The lower triangle has an area of 1/2 × 2 × 13 = 13. Adding these areas, we get the area for the quadrilateral: 52 + 26 + 13 = 91. Again, we see that the correct answer is choice (A).  If the y coordinates are 2 and 6 then the length of the left side is 9 and the right side is 7 (you need to count the 0)! Area = 1/2 × (9+7) × 13 = 104 (and not 91) 
Author:  Gennadiy [ Wed Jun 09, 2010 4:55 pm ]  
Post subject:  Re: GMAT Coordinate Geometry  
It may be easier if you break each segment in two. Segment that connects points (2, 2) and (2, 6) we can break into (2, 0)  (2, 6) segment, length 6 & (2, 2)  (2, 0) segment, length 2. The total length is 8. The same works for the right side.

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