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In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar

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In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar  [#permalink]

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New post Updated on: 06 Oct 2016, 06:27
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A
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  45% (medium)

Question Stats:

74% (02:12) correct 26% (02:14) wrong based on 78 sessions

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In the diagram below, BD = 8, AB = 6, and ED = 5. What is the area of ABCE?
Attachment:
rectangle_triangle.gif
rectangle_triangle.gif [ 2.54 KiB | Viewed 1384 times ]


(A) 16
(B) 18
(C) 20
(D) 22
(E) 24

Originally posted by NaeemHasan on 03 Oct 2016, 05:57.
Last edited by NaeemHasan on 06 Oct 2016, 06:27, edited 1 time in total.
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Re: In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar  [#permalink]

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New post 03 Oct 2016, 06:38
Ans is 24
Steps :
Since we know AB = 6 ; BD =8 and it is right angle triangle.. we can find AD =10 ;
Given ED=5 So AE=5;(AE+ED=10)
ABD and ECD are Similar triangle as they have 30 and 90 Degree in common, with that we can find EC=3
AB=FC=6;
FC= EC+EF ; So EF=3
EF=3 Ae=5
AF=4;
Area of rectangle = AB * AF = 6*4 =24
Is this Right ?
Is there any easy way to do it ?
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Re: In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar  [#permalink]

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New post 03 Oct 2016, 08:20
Shrivathsan wrote:
Ans is 24
Steps :
Since we know AB = 6 ; BD =8 and it is right angle triangle.. we can find AD =10 ;
Given ED=5 So AE=5;(AE+ED=10)
ABD and ECD are Similar triangle as they have 30 and 90 Degree in common, with that we can find EC=3
AB=FC=6;
FC= EC+EF ; So EF=3
EF=3 Ae=5
AF=4;
Area of rectangle = AB * AF = 6*4 =24
Is this Right ?
Is there any easy way to do it ?



Area of AEF = \(\frac{1}{2}\) * AF * FE = \(\frac{1}{2}\) * 4 * 3 = 6

We need to find the area of ABCE = Area of rectangle ABCF - Area of triangle AEF = 24-6 = 18.

I think answer should be B
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Re: In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar  [#permalink]

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New post 03 Oct 2016, 08:47
0ld wrote:
We need to find the area of ABCE


Oops .. i read the question wrong..
Ya then answer is 18 as ABCE resembles a trapezium.
So area is 1/2 * 9 *4 =18
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Shri
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Re: In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar  [#permalink]

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New post 10 Sep 2018, 14:05
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Re: In the diagram below, BD = 8, AB = 6, and ED = 5. What is the ar   [#permalink] 10 Sep 2018, 14:05
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