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The area of region ABCD [#permalink]
15 Dec 2016, 02:23

Expert's post

00:00

Question Stats:

63% (00:41) correct
36% (00:36) wrong based on 22 sessions

Attachment:

#GREpracticequestion ABCD is a parallelogram.jpg [ 5.26 KiB | Viewed 944 times ]

ABCD is a parallelogram

Quantity A

Quantity B

The area of the region ABCD

24

A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.

Re: The area of region ABCD [#permalink]
29 Dec 2016, 13:45

3

This post received KUDOS

Expert's post

Carcass wrote:

ABCD is a parallelogram

Quantity A

Quantity B

The area of the region ABCD

24

First notice that IF a RECTANGLE had lengths the same as the parallelogram...

...then the area of that rectangle would be 24 (since area = base x height = 4x6 = 24)

However, the given quadrilateral is NOT a rectangle. Instead, the rectangle has been "pushed" over.

Notice that if we "push" the rectangle far enough, then its measurements will be the same as in the given diagram/

Most importantly, the height is now less than 6 The area of a parallelogram = base x height So, the area = 4 x (some number that's less than 6) = some value that's less than 24

ASIDE: We need not find the actual height of the parallelogram; we need only recognize that it will be less than 6.

We have: Quantity A: some value that's less than 24 Quantity B: 24

Answer: B
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Re: The area of region ABCD [#permalink]
05 Dec 2018, 19:54

Expert's post

msk0657 wrote:

Carcass..if not above logic , what could be the other solution.

see what can be the area of the given parallelogram.. The area of a parallelogram is Base * Height. Base is 4 and height is a, which will be less than 6 as 6 is the hypotenuse and thus he largest side of right angled triangle. therefore area will be < 4*6 or <24. hence B>A.

Re: The area of region ABCD [#permalink]
06 Dec 2018, 01:13

It's quite simple. The area of a parallelogram will be 6x4xSin125. That's 24Sin125. The value of Sin125 should be less than 1. That will reduce the area below 24. So 24 is more than 24 Sin125. It's B

Re: The area of region ABCD [#permalink]
14 Feb 2019, 12:46

1

This post received KUDOS

Expert's post

Carcass wrote:

Attachment:

#GREpracticequestion ABCD is a parallelogram.jpg

ABCD is a parallelogram

Quantity A

Quantity B

The area of the region ABCD

24

A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.

Here's a different approach:

The area of a parallelogram = (base)(height)

We know the base has length 4...

...however, we don't know the height:

However, if we recognize that we have a RIGHT TRIANGLE hiding in our diagram...

... we can use the fact that the hypotenuse is always the longest side in a RIGHT TRIANGLE. Since the hypotenuse in the above triangle has length 6, we know that the other sides of the right triangle are LESS THAN 6

This means the triangle's height is less than 6

It also means the height of the parallelogram is less than 6

We're now ready to answer the question.

The area of a parallelogram = (base)(height) = (4)(some number less than 6) = some number less than 24

So, we get: QUANTITY A: some number less than 24 QUANTITY B: 24

Answer: B

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Re: The area of region ABCD
[#permalink]
14 Feb 2019, 12:46