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What is the area of the triangle in the figure above?

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What is the area of the triangle in the figure above?  [#permalink]

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New post 27 Dec 2015, 10:42
1
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A
B
C
D
E

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  85% (hard)

Question Stats:

55% (02:45) correct 45% (02:50) wrong based on 128 sessions

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What is the area of the triangle in the figure above?  [#permalink]

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New post 29 Dec 2015, 00:47
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Bunuel wrote:
Image
What is the area of the triangle in the figure above?

A. \(2+2\sqrt{3}\)
B. \(4\sqrt{3}\)
C. 8
D. \(8\sqrt{3}\)
E. 12

Attachment:
The attachment 2015-12-27_2141.png is no longer available



Hi,
the Q may be 700+, since you require to know to play around with Geometrical figures..
the best way is to look how we can draw a 90 degree angle , which will help us to break the figure down to simpler terms
[img]http://gmatclub.com/forum/download/file.php?mode=view&id=28776[/img]..
here we see the third angle C shouold be 45, so we draw a perpendicular from B to AC..
now we have two triangles ABD and BCD..
lets see the first triangle BCD..
angle BCD and CBD are 45 and CDB is 90...
\(Hyp = BC= 2\sqrt{2}\)...
so the sides BD and CD=2..
area of BCD=1/2 * 2*2=2...

lets see the second triangle ABD..
it is 30-60-90 triangle...
and therefore the sides BD:AD:AB are in ratio \(1:\sqrt{3}:2\)..
BD is 2, so AD = \(2\sqrt{3}\)..
so \(area = 1/2 * 2\sqrt{3}*2=2\sqrt{3}\)..

\(total Area=2+ 2\sqrt{3}\)
ans A
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ANGLES.png [ 24.18 KiB | Viewed 2050 times ]


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Re: What is the area of the triangle in the figure above?  [#permalink]

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New post 01 Jan 2016, 12:11
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Hi All,

Since the GMAT is built around existing patterns/rules/logic, the Geometry questions that you face on Test Day will almost always be based on standard shapes and formulas that you already know (or should know). Any time a question involves a shape that is 'weird', that shape can almost always be broken-down into smaller standard shapes - you can then use your knowledge of those shapes to answer the given question (although the math involved might be 'step-heavy').

Here, the weird shape is a 30/45/105 triangle. As chetan2u pointed out in his explanation, this triangle can be split into a 30/60/90 and a 45/45/90. From there, you can use the given side length, along with the rules for those 2 right triangles, to figure out ALL of the other side lengths and the total area of the shape.

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Re: What is the area of the triangle in the figure above?  [#permalink]

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New post 24 Sep 2018, 07:57
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Re: What is the area of the triangle in the figure above?   [#permalink] 24 Sep 2018, 07:57
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