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805+ (Hard)|   Geometry|      
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Bunuel
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In parallelogram ABCD, point E is the midpoint of side AD and point F 06 Dec 2021, 02:30
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32% (02:10) correct 68% (02:09) wrong based on 66 sessions

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In parallelogram ABCD, point E is the midpoint of side AD and point F is the midpoint of side CD. If point G is the midpoint of line segment ED and point H is the midpoint of line segment DF, what is the area of triangle DGH ?

(1) Parallelogram ABCD has an area of 96.
(2) The parallelogram has sides of lengths 8 and 12.


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A
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In parallelogram ABCD, point E is the midpoint of side AD and point F 06 Dec 2021, 09:14
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Bunuel
In parallelogram ABCD, point E is the midpoint of side AD and point F is the midpoint of side CD. If point G is the midpoint of line segment ED and point H is the midpoint of line segment DF, what is the area of triangle DGH ?

(1) Parallelogram ABCD has an area of 96.
(2) The parallelogram has sides of lengths 8 and 12.


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I chose D but I'm not sure if it's correct

1 - It seems that since a parallelogram would divide equally in two triangles cut in the middle - each would have an area of 96/2. Continuing this we could get the smaller triangle's area - so Sufficient
2 - We get the 2 sides of the triangle and the including angle - With two angles and a side we can find most things about a triangle since it is unique so I assumed that this would be sufficient too
Hence D.
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In parallelogram ABCD, point E is the midpoint of side AD and point F 06 Dec 2021, 23:16
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I believe the answer would be A.
As with the help of statement A we can calculate area 96/4*4=12.
But for calculating area from statement 2 we will be needing angle between them.
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In parallelogram ABCD, point E is the midpoint of side AD and point F 29 Jun 2022, 19:31
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OA from Princeton review
This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Begin by determining “What is known” from the question stem and “What is needed” from the statements to answer the question. Determine “What is known.” The question asks for the area of triangle DGH. Draw and label parallelogram ABCD such that line segment AD represents the base of the parallelogram. Add points E, F, G, and H to the figure, so that line segment GD represents the base of triangle DGH, which occupies the parallelogram’s lower right corner. Whether or not the parallelogram is rectangular, the base of triangle DGH is one-fourth the base of parallelogram ABCD, and the height of triangle DGH is one-fourth the height of parallelogram ABCD. If bh represents the area of parallelogram ABCD, then the area of triangle DGH is 1/2(1/4b)(1/4h) , or 1/32bh. Now, determine “What is needed.” In order to answer the question, the statement(s) must provide information sufficient to determine either the area of parallelogram ABCD or the base and height of triangle DGH. Evaluate the statements one at a time.

Evaluate Statement (1). If the area of parallelogram ABCD is 96 square units, then the area of triangle DGH is 1/32 *96 = 3 square units. Statement (1) is sufficient to answer the question, so write down AD.

Now, evaluate Statement (2). If the parallelogram is a rectangle with dimensions 8 by 12, then the base and height of triangle DGH are 2 and 3, and the area of the triangle is square units. However, if parallelogram ABCD is not a rectangle, then its sides are not perpendicular. In this case, the measures of the parallelogram’s interior angles are unknown, so it is impossible to determine the parallelogram’s height, and impossible to determine the triangle’s height. Statement (2) is insufficient to answer the question, so eliminate choice D. The correct answer is choice A.
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In parallelogram ABCD, point E is the midpoint of side AD and point F 01 Sep 2023, 09:34
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CYp113
OA from Princeton review
This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Begin by determining “What is known” from the question stem and “What is needed” from the statements to answer the question. Determine “What is known.” The question asks for the area of triangle DGH. Draw and label parallelogram ABCD such that line segment AD represents the base of the parallelogram. Add points E, F, G, and H to the figure, so that line segment GD represents the base of triangle DGH, which occupies the parallelogram’s lower right corner. Whether or not the parallelogram is rectangular, the base of triangle DGH is one-fourth the base of parallelogram ABCD, and the height of triangle DGH is one-fourth the height of parallelogram ABCD. If bh represents the area of parallelogram ABCD, then the area of triangle DGH is 1/2(1/4b)(1/4h) , or 1/32bh. Now, determine “What is needed.” In order to answer the question, the statement(s) must provide information sufficient to determine either the area of parallelogram ABCD or the base and height of triangle DGH. Evaluate the statements one at a time.

Evaluate Statement (1). If the area of parallelogram ABCD is 96 square units, then the area of triangle DGH is 1/32 *96 = 3 square units. Statement (1) is sufficient to answer the question, so write down AD.

Now, evaluate Statement (2). If the parallelogram is a rectangle with dimensions 8 by 12, then the base and height of triangle DGH are 2 and 3, and the area of the triangle is square units. However, if parallelogram ABCD is not a rectangle, then its sides are not perpendicular. In this case, the measures of the parallelogram’s interior angles are unknown, so it is impossible to determine the parallelogram’s height, and impossible to determine the triangle’s height. Statement (2) is insufficient to answer the question, so eliminate choice D. The correct answer is choice A.
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Hey CYp113, can you please explain how does the height of the triangle become the 1/4 of the height of the parallelogram? I mean the base remains constant for both the geometric figures but then the height of the triangle will lie on the other side of the parallelogram right? and how do we know whether it is an altitude or just another random line? Can you please help me understand, hopefully through a pictorial representation? Thanks a lot. :)
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