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In the figure, what is the area of triangle BCD given that the area of

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Bunuel
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In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   10 May 2018, 01:39
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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


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D
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BrentGMATPrepNow
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In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   Updated on: 28 Apr 2021, 06:41
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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

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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


Answer: D

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Originally posted by BrentGMATPrepNow on 19 Oct 2018, 14:01.
Last edited by BrentGMATPrepNow on 28 Apr 2021, 06:41, edited 1 time in total.
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Re: In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   10 May 2018, 05:42
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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.

Answer: D
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Re: In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   19 Oct 2018, 14:52
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?

Thanks in advance
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Re: In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   21 Oct 2018, 10:23
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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?

Thanks in advance


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.
More here: https://en.wikipedia.org/wiki/Cyclic_quadrilateral

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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Re: In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   22 Oct 2018, 05:42
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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Re: In the figure, what is the area of triangle BCD given that the area of [#permalink] New post   15 May 2022, 23:51
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Re: In the figure, what is the area of triangle BCD given that the area of [#permalink]
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