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01 May 2018, 05:39
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:56) correct
37%
(02:43)
wrong
based on 231
sessions
History
Date
Time
Result
Not Attempted Yet
Trapezoid OPQR has one vertex at the origin. What is the area of OPQR ?
A. \(\frac{a^2}{4}\)
B. \(\frac{a^2}{2}\)
C. \(\frac{3a^2}{4}\)
D. \(\frac{3a^2}{2}\)
E. \(2a^2\)
Attachment:
axis.jpg [ 17.11 KiB | Viewed 9896 times ]
Bunuel
Lets extend RQ till Y-axis , and this extension meets y-axis at pt A.
Thus coordinate of A = (0,a)
Now as O is the orgin the co-ordinate of O =(0,0)
now, in in triangle AOR & APQ,
angle A is same for both & PQllOR (as the figure is trapezoid) & AR=2AQ(given)
Thus by triangle properties AO=2AP.......................................................................Please closely refer the diagram provided in the Q-stem
Thus AR = 2a, AQ=a & AO=a & AP=a/2
Area of trapezoid = area of triangle ARO - area of triangle AQP = \(\frac{1}{2}*AR*AO\) - \(\frac{1}{2}*AQ*AP\) =\(\frac{1}{2}*2a*a\) - \(\frac{1}{2}*a*\frac{a}{2}\) = \(a^2\) - \(\frac{a^2}{4}\) = \(\frac{3a^2}{4}\)......Hence the answer is C
General Discussion
01 May 2018, 19:37
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Smart guessing approach :
A (of trapezoid) = A (of rectangle) - A (triangle 1) - A (triangle 2)
Let a= 2, then A (of trapezoid) = 2*4 -1/2*2*4-1/2*2*1 = 3, where (1 - is estimated length, which lays in the range from 0 to 2)
Subsrituting with a=2 answer options
A 1
B 2
C 3 - closest, let's pick it.
D 6
E 8
This is not the best approach, but it works in most of the cases, when you have no clue how to solve the problem. You have to never give up.
A (of trapezoid) = A (of rectangle) - A (triangle 1) - A (triangle 2)
Let a= 2, then A (of trapezoid) = 2*4 -1/2*2*4-1/2*2*1 = 3, where (1 - is estimated length, which lays in the range from 0 to 2)
Subsrituting with a=2 answer options
A 1
B 2
C 3 - closest, let's pick it.
D 6
E 8
This is not the best approach, but it works in most of the cases, when you have no clue how to solve the problem. You have to never give up.
Attachments
axis.jpg [ 13.3 KiB | Viewed 9175 times ]
