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# Let ABCD be a parallelogram. Determine the area of the DOC triangle...

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Intern
Joined: 02 Mar 2020
Posts: 6
Let ABCD be a parallelogram. Determine the area of the DOC triangle...  [#permalink]

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Updated on: 24 May 2020, 19:44
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Difficulty:

55% (hard)

Question Stats:

67% (01:37) correct 33% (01:58) wrong based on 6 sessions

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Let ABCD be a parallelogram. Determine the area of the DOC triangle that is contained in it.
(1) The area of the parallelogram is 84 cm2.
(2) "O" is the point that is exactly in the middle of the AB side.

I think the answer is "E" because I do not have an indication of the proportion of the base and height values, and the area A=b*a=84*1=42*2=28*3=21*4=14*6=12*7=84. I don't understand why the official answer is "A".

Originally posted by mmejiaherrera on 24 May 2020, 16:46.
Last edited by chetan2u on 24 May 2020, 19:44, edited 1 time in total.
Corrected the OA
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Joined: 19 Oct 2018
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Let ABCD be a parallelogram. Determine the area of the DOC triangle...  [#permalink]

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24 May 2020, 19:29
1
Whoever wrote this made an assumption that O lies somewhere on AB.

Statement 1.

Area of parallelogram = h*CD = 84

It doesn't matter where O lies on AB; Height of altitude drawn from O to CD is always equal to h.

Area of DOC = 1/2*h * CD = 42

Sufficient

Statement 2- We don't know any dimension of parallelogram or triangle; We can't find area.

Insufficient

mmejiaherrera wrote:
Let ABCD be a parallelogram. Determine the area of the DOC triangle that is contained in it.
(1) The area of the parallelogram is 84 cm2.
(2) "O" is the point that is exactly in the middle of the AB side.

I think the answer is "E" because I do not have an indication of the proportion of the base and height values, and the area A=b*a=84*1=42*2=28*3=21*4=14*6=12*7=84. I don't understand why the official answer is "A".

Attachments

Untitled.png [ 2.98 KiB | Viewed 146 times ]

Math Expert
Joined: 02 Aug 2009
Posts: 8755
Re: Let ABCD be a parallelogram. Determine the area of the DOC triangle...  [#permalink]

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24 May 2020, 19:44
1
mmejiaherrera wrote:
Let ABCD be a parallelogram. Determine the area of the DOC triangle that is contained in it.
(1) The area of the parallelogram is 84 cm2.
(2) "O" is the point that is exactly in the middle of the AB side.

I think the answer is "E" because I do not have an indication of the proportion of the base and height values, and the area A=b*a=84*1=42*2=28*3=21*4=14*6=12*7=84. I don't understand why the official answer is "A".

The way it is written, the answer should be C.

See the sketch O can be anywhere, so area could be anything.

(1) The area of the parallelogram is 84 cm2.
But we do not know where does O lie. We know CD is common but the height is not known.

(2) "O" is the point that is exactly in the middle of the AB side.
Now we know that the area of ABCD = CD*h. and area of DOC=$$\frac{1}{2}*CD*h$$, so half of ABCD.
But we do not know the area of parallelogram.

Combined.
Area = 42

C
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Untitledaba.png [ 8.06 KiB | Viewed 140 times ]

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Joined: 02 Mar 2020
Posts: 6
Let ABCD be a parallelogram. Determine the area of the DOC triangle...  [#permalink]

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24 May 2020, 20:24
Hi! Sorry, my account doesn't have picture privileges.
The "O" point is the midpoint of the AB line, that is:
A-------O-------B
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File comment: Here's the picture, I finally managed to upload it.

Parallelogram.jpg [ 13.19 KiB | Viewed 92 times ]

Let ABCD be a parallelogram. Determine the area of the DOC triangle...   [#permalink] 24 May 2020, 20:24

# Let ABCD be a parallelogram. Determine the area of the DOC triangle...

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