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Parallelogram and Area

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by coolhabhi » Fri Nov 25, 2016 6:15 am
ABCD is a trapezium with AD & BC as parallel sides. E is a point on BC in such a way that ABED becomes a parallelogram. The ratio of the area of ABED to that of ABCD is

a) (AD + BC)/(AD + BE)
b) (AD + BE)/(AD + BC)
c) BE/BC
d) BC/BE
e) AD/BC

OE B
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by GMATGuruNY » Fri Nov 25, 2016 7:21 am
coolhabhi wrote:ABCD is a trapezium with AD & BC as parallel sides. E is a point on BC in such a way that ABED becomes a parallelogram. The ratio of the area of ABED to that of ABCD is

a) (AD + BC)/(AD + BE)
b) (AD + BE)/(AD + BC)
c) BE/BC
d) BC/BE
e) AD/BC

OE B
Let ABCD and ABED look as follows:
Image

Area of parallelogram ABED = bh = (AD)(EF) = 2*1 = 2.
Area of trapezoid ABCD = (b� + b₂)/2 * h = (AD + BC)/2 * EF = (2+4)/2 * 1 = 3.
(ABED)/(ABCD) = 2/3. This is our target.

Now check the answer choices to see which yields our target of 2/3.
Only B works:
(AD + BE)/(AD + BC) = (2 + 2)/(4 + 2) = 4/6 = 2/3.

The correct answer is B.
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by Jay@ManhattanReview » Wed Dec 28, 2016 4:37 am
coolhabhi wrote:ABCD is a trapezium with AD & BC as parallel sides. E is a point on BC in such a way that ABED becomes a parallelogram. The ratio of the area of ABED to that of ABCD is

a) (AD + BC)/(AD + BE)
b) (AD + BE)/(AD + BC)
c) BE/BC
d) BC/BE
e) AD/BC

OE B
I suggest you draw a trapezium such that AD & BC are its parallel sides and BC is the longest side. It is given that E is a point on BC such that ABED becomes a parallelogram.

We know that area of trapezium ABCD = (Sum of parallel sides) * Height = (AD + BC) * Height;

Area of parallelogram ABED = (Sum of parallel sides) * Height = (AD + BE) * Height;

=> Ratio of the area of ABED to that of ABCD = [(AD + BE) * Height] / [(AD + BC) * Height]

=> Ratio of the area of ABED to that of ABCD = (AD + BE) / (AD + BC)

OA: B

-Jay

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