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In the rectangle above, A is the midpoint of the side, and

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In the rectangle above, A is the midpoint of the side, and [#permalink] New post 15 Aug 2011, 01:57
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A
B
C
D
E

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Question Stats:

31% (02:51) correct 69% (00:21) wrong based on 20 sessions
In the rectangle above, A is the midpoint of the side, and BC=CD=DE. What is the area of the rectangle?
(1) The area of the shaded region is 24.
(2) The area of triangle CDO is 16.

I got the answer but need a more concise approach..

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Last edited by DeeptiM on 15 Aug 2011, 06:06, edited 1 time in total.
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Re: Geometry!! [#permalink] New post 15 Aug 2011, 05:58
Consider this, area for triangle is BH/2.

the two bigger triangles have the same B & H, the three small triangles have the same base and height. thus we can say the three smaller triangles or the 2 larger are equal. with (1) or (2) we can see the area of the full rectangle is 96.

(18*3)*2 or (24*2)*2
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Re: Geometry!! [#permalink] New post 15 Aug 2011, 06:10
well u wld hve to b a lil patient wid me...

somehow um still unclear with the explanation :(
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Re: Geometry!! [#permalink] New post 15 Aug 2011, 07:08
DeeptiM wrote:
well u wld hve to b a lil patient wid me...

somehow um still unclear with the explanation :(


D from my side.

1. Area of rectangle = 2*2*Area(AOB) - Suff.
2. Area of rectangle = 2*3*Area COD (because Area BOC= Area COD= Area DOC) - Suff.

Hope it helps.

Cheers,
Aj.

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Re: Geometry!! [#permalink] New post 15 Aug 2011, 07:40
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DeeptiM wrote:
In the rectangle above, A is the midpoint of the side, and BC=CD=DE. What is the area of the rectangle?
(1) The area of the shaded region is 24.
(2) The area of triangle CDO is 16.

I got the answer but need a more concise approach..

Attachment:
Geomtery_Median_DS.JPG


Let's call the vertex diagonally opposite of E as F.

1.
OA is the median of \triangle OBF, because A is the mid-point of FB. A median divides a triangle in two-halves such that the areas of two newly formed triangles are equal.

Area(OAF)=Area(OAB)=24
Area(OBF)=2*Area(OAB)=2*24=48

A diagonal of a rectangle divides the rectangle in two equal halves such that the area remains same for both halves.

Thus, Area(ABEO)=2*Area(BOF)=2*48=96
Sufficient.

2.
Same concept as statement 1.
OD is the median of OCE because CD=DE
AND
OC is the median of OBD because CD=BC

Area(ODE)=Area(OCD)=Area(OCB)=16
Area(OBE)=3*16=48
Area(FBEO)=2*Area(OBE)=2*48=96
Sufficient.

Ans: "D"

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Re: Geometry!!   [#permalink] 15 Aug 2011, 07:40
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In the rectangle above, A is the midpoint of the side, and

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