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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
In the figure, what is the area of triangle BCD given that the area of  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 53% (01:44) correct 47% (02:24) wrong based on 110 sessions

HideShow timer Statistics In the figure, what is the area of triangle BCD given that the area of triangle ADE is 16 and the area of triangle CDE is 12?

A) 12
B) 16
C) 20
D) 28
E) Cannot be determined

Attachment: FIGURE.jpg [ 24.33 KiB | Viewed 2068 times ]

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: In the figure, what is the area of triangle BCD given that the area of  [#permalink]

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Solution

Given:
• Area of triangle ADE = 16
• Area of triangle CDE = 12

To find:
• What is the area of triangle BCD

Approach and Working:
• As the triangles ACD and BCD share the same base DC, and their height is also same, they have equal area
• Therefore, the area of triangle BCD = area of triangle ACD = area of triangle ADE + area of triangle CDE = 16 + 12 = 28

Hence, the correct answer is option D.

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: In the figure, what is the area of triangle BCD given that the area of  [#permalink]

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Bunuel wrote: In the figure, what is the area of triangle BCD given that the area of triangle ADE is 16 and the area of triangle CDE is 12?

A) 12
B) 16
C) 20
D) 28
E) Cannot be determined

Attachment:
FIGURE.jpg

∆ADC is comprised of 2 regions: ∆ADE and ∆CDE
We're told that ∆ADE and ∆CDE have areas 16 ans 12 respectively.
So, the area of ∆ADC = 16 + 12 = 28 First recognize that ∆ADC and ∆BCD both have the same base.
Also, if we let h = the height of ∆ADC, then ∆BCD also has height h area of triangle = (base)(height)/2
So, if ∆ADC and ∆BCD have the same base and the same height, then they must have the same area.

So, if the area of ∆ADC is 28, then the area of ∆BCD must also be 28

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Joined: 26 Mar 2013
Posts: 2345
Re: In the figure, what is the area of triangle BCD given that the area of  [#permalink]

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Dear GMATPrepNow Brent

I have general question about irregular quadratic like the above, the sum of interior angles is 360 but does this mean the sum of opposite angles MUST equal to 180? Citing the graph above, does A+C =180 or B+D=180?

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: In the figure, what is the area of triangle BCD given that the area of  [#permalink]

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Top Contributor
Mo2men wrote:
Dear GMATPrepNow Brent

I have general question about irregular quadratic like the above, the sum of interior angles is 360 but does this mean the sum of opposite angles MUST equal to 180? Citing the graph above, does A+C =180 or B+D=180?

I believe the rule you're referring to involves a very special kind of quadrilateral, one that is inscribed in a circle (aka a cyclic quadrilateral)
In that very special case, the opposite angles add to 180.

Cyclic quadrilaterals are not tested on the GMAT, so you won't encounter a question in which the correct answer depends solely on this rule.

Cheers,
Brent
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Joined: 05 Jan 2017
Posts: 34
Re: In the figure, what is the area of triangle BCD given that the area of  [#permalink]

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AB and DC are parallel as both make 90 deg on lie AD
for triangle ADC and BCD the base is same and the height is also same. hence the area is also same
we just need to find the area of ADC
16+12 = 28 (D)
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Kudos if my post helps! Re: In the figure, what is the area of triangle BCD given that the area of   [#permalink] 22 Oct 2018, 05:42
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