GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the figure above, what is the area of triangle BCD given
[#permalink]
08 Feb 2018, 00:54
08 Feb 2018, 00:54
2
8
Bookmarks
00:00
Question Stats:
61% (01:54) correct
38% (02:52) wrong based on 36 sessions
Hide Show timer Statistics
In the figure, what is the area of triangle BCD given that the area of triangle ADE is 16 & the area of triangle CDE is 12?
A) 12
B) 16
C) 20
D) 28
E) Cannot be determined
src: Brightlink Prep
A) 12
B) 16
C) 20
D) 28
E) Cannot be determined
src: Brightlink Prep
Show: ::
D
Attachments
FIGURE.jpg [ 24.33 KiB | Viewed 7531 times ]
Sherpa Prep Representative
Joined: 15 Jan 2018
Posts: 147
Given Kudos: 0
Re: In the figure above, what is the area of triangle BCD given
[#permalink]
08 Feb 2018, 08:50
08 Feb 2018, 08:50
2
Expert Reply
The area of a triangle is (1/2)bh. But we don't know the base or height of triangle BCD. Is there a way to find them? Always take note of any shapes in a picture, especially the shapes that aren't mentioned. Notice that there is another triangle with the same base and height as triangle BCD, i.e. triangle ADC. Since it has the same base and same height, it must have the same area. And since triangle ADC is simply triangles ADE and CDE stuck together, we can add their areas to get the answer. Since 16 + 12 is 28, D is the answer.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the figure above, what is the area of triangle BCD given
[#permalink]
28 Apr 2021, 05:41
28 Apr 2021, 05:41
amorphous wrote:
In the figure, what is the area of triangle BCD given that the area of triangle ADE is 16 & the area of triangle CDE is 12?
A) 12
B) 16
C) 20
D) 28
E) Cannot be determined
A) 12
B) 16
C) 20
D) 28
E) Cannot be determined
Show: ::
D
∆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
