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square root of the area of Trapezoid- Pls help

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by kishokbabu » Mon Dec 12, 2011 6:42 am
In a rectangular co-ordinate system, what is the square root of the area of a trapezoid whose vertices have the co-ordinates (2,2), (2,3),(20,2),(20,-2)?

Answer choices are .: a)7 b) 9 c) 10.22, d) 12.25 e) 14

correct answer choice is B-9

can anyone explain me how to solve this problem in some easy steps?
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by Elena89 » Mon Dec 12, 2011 7:20 am
kishokbabu wrote:In a rectangular co-ordinate system, what is the square root of the area of a trapezoid whose vertices have the co-ordinates (2,2), (2,3),(20,2),(20,-2)?

Answer choices are .: a)7 b) 9 c) 10.22, d) 12.25 e) 14

correct answer choice is B-9

can anyone explain me how to solve this problem in some easy steps?
Here's what you do:

First draw the trapezoid in the xy-plane according to the four ordered pairs.

You'll get a figure like the one attached. Take the two parallel sides as the two bases. And draw the perpendicular from one parallel side to the other. This is the height. Now just plug in values in the formula for area of a trapezoid [(Base 1 + Base 2)/2]*Height:

[(4+5)/2]*18 = 81

And root of 81 = 9

And so the answer is option B) 9
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Last edited by Elena89 on Mon Dec 12, 2011 9:39 am, edited 1 time in total.
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by cpschott » Mon Dec 12, 2011 9:11 am
image is misleading, line h should intersect two vertices- (2,2) and (20,2)

then i have one triangle with area =1X18/2
and the second with area =4X18/2

18/2 + 72/2= 45
sqrt(45) = <7

what gives-- would need points at (2,2); (2,6); (20,2); (20,-3) to get 9
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by user123321 » Mon Dec 12, 2011 9:13 am
i think area should be 45 with those coordinates.
i am not sure where i did mistake. can you check the coordinates once again?

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by Elena89 » Mon Dec 12, 2011 9:44 am
my bad! with these coordinates, the area is indeed 45. :?
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by GMATGuruNY » Mon Dec 12, 2011 10:44 am
kishokbabu wrote:In a rectangular co-ordinate system, what is the square root of the area of a trapezoid whose vertices have the co-ordinates (2,2), (2,3),(20,2),(20,-2)?

Answer choices are .: a)7 b) 9 c) 10.22, d) 12.25 e) 14

correct answer choice is B-9

can anyone explain me how to solve this problem in some easy steps?
The problem has been transcribed incorrectly.
The intended coordinates are (2,-2), (2,3), (20,2) and (20,-2).

Thus:
b1 = 3-(-2) = 5.
b2 = 2-(-2) = 4.
h = 20-2 = 18.
Area = (b1 + b2)/2 * h = (5+4)/2 * 18 = 81.
√81 = 9.

The correct answer is B.
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