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In the figure above, what is the area of triangle BCD given
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08 Feb 2018, 00:54
08 Feb 2018, 00:54
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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
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Re: In the figure above, what is the area of triangle BCD given
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08 Feb 2018, 08:50
08 Feb 2018, 08:50
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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.
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Re: In the figure above, what is the area of triangle BCD given
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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
