Hero8888 wrote:
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.
You don't need to guess here. The approach is absolutely valid.
Note that we have a trapezoid which means PQ is parallel to OR.
The co-ordinates of R are (2a, a) which means for an increase of 2a in x, y increased by a i.e. half. So slope of OR is 1/2.
Then slope of PQ is 1/2 too. Since from P to Q, x co-ordinate increases by a, the y co-ordinate must have increased by a/2. So y co-ordinate of P must be a/2.
Then if a = 2, P is (0, 1), Q is (2, 2) and R is (4, 2).
A (of trapezoid) = A (of rectangle) - A (triangle 1) - A (triangle 2)
A (of trapezoid) = 4*2 - (1/2)*1*2 - (1/2) * 4*2 = 3
Put a = 2 in options to get 3 for option (C).
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Karishma
Veritas Prep GMAT Instructor
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