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What is the area of the shaded portion of this rectangle, given that A

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Bunuel
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What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  31 Jan 2016, 07:02
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What is the area of the shaded portion of this rectangle, given that AD = 6, CD = 8, and AE = x?

A. 48 − 3x
B. 48 + 3x
C. 3x + 16
D. 24 − 3x
E. 24 + 3x

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2016-01-31_1801.png
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EMPOWERgmatRichC
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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  01 Feb 2016, 11:35
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Hi All,

This question can be solved by TESTing VALUES. Here are a couple of hints so that you can try this question on your own:

Show Spoiler
1) To find the area of the shaded region, you need to subtract the area of the white triangle from the area of the rectangle.
2) TEST a VALUE for X - remember that since AB=CD=8, X has to be less than 8).
3) Calculate the area of the triangle and subtract it from the area of the rectangle.
4) Find the 'matching' value in the answer choices.


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Mo2men
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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  02 Feb 2016, 18:23
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Hi Rich,

In this question particularly, I think the answer choices reveal the answer. The shaded area should be result of subtracting rectangular area from the area of triangle.

The only choice that contain area of rec (48) is choice (A)

If the choices have more 48, we may use Testing the Values
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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  02 Feb 2016, 23:29
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Hi Mo2men,

You bring up a very good point. Whoever wrote the answer choices to this question really made it 'easy' for you to spot that pattern. However, you will likely NOT have it so easy on the multi-shape Geometry question(s) that you face on the Official GMAT. Those questions can be some of the most time-consuming and toughest questions that you face. As such, you'll still need to be practicing the proper math 'skills' and Tactics to consistently score at a high level in the Quant section.

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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  04 Feb 2016, 02:54
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Bunuel wrote:

What is the area of the shaded portion of this rectangle, given that AD = 6, CD = 8, and AE = x?

A. 48 − 3x
B. 48 + 3x
C. 3x + 16
D. 24 − 3x
E. 24 + 3x

Show Spoiler
Attachment:
2016-01-31_1801.png


Whenever you see a question with shaded area, try to find out the area of the participating figures.
In this case, we need the area of the rectangle ABCD and triangle ADE

1. Area of rectangle = AD*CD = 6*8 = 48
2. Area of triangle = \(\frac{1}{2}\)* AD*AE = \(\frac{1}{2}\) *6*x = 3x

Area of shaded region = area of rectangle - area of triangle = 48 - 3x (Option A)
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What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  04 Feb 2016, 12:59
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The solutions above are perfect, and probably the easiest way to go. I agree with Rich that on the actual test you're probably not going to be so lucky as to see answer choices as straightforward as these.

Another approach would be to calculate the area of the shaded region directly using the formula for the area of a trapezoid.

\(A=\frac{l_1+l_2}{2}*h\) where \(l_1\) and \(l_2\) are the lengths of the parallel sides, and \(h\) is the height (perpendicular distance between the parallel sides)

\(A=\frac{8+(8-x)}{2}*6\)

\(A=(8-\frac{x}{2})*6\)

\(A = 48-3x\)

Answer: A
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sharmilaz87
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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  04 Feb 2016, 20:16
Area of the rectangle ABCD=6*8=48
Let AE=x, since AB=8, EB=8-x
EBCD is a trapezoid
Area of EBCD=(Base1+Base2)/2 * Height={8+(8-x)}/2 * 6=48-3x
Ans.A
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What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  27 Oct 2020, 16:34
Area of shaded portion = Total area - Area of triangle AED

Total area = 6 * 8 = 48

Area of Triangle AED = \(\frac{1}{2}\) * x * 6 = 3X

Therefore , area of shaded portion = 48 - 3X

Answer A
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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink] New post  31 Oct 2020, 13:50
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Bunuel wrote:

What is the area of the shaded portion of this rectangle, given that AD = 6, CD = 8, and AE = x?

A. 48 − 3x
B. 48 + 3x
C. 3x + 16
D. 24 − 3x
E. 24 + 3x

Show Spoiler
Attachment:
2016-01-31_1801.png

Solution:

We see that the area of the shaded region is the difference between the area of rectangle ABCD and the area of triangle ADE.

Since the area of rectangle ABCD is 8 * 6 = 48 and the area of triangle ADE is ½ * 6 * x = 3x, the area of the shaded region is 48 - 3x.

Answer: A
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Re: What is the area of the shaded portion of this rectangle, given that A [#permalink]
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