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In the figure above AD = 4, AB = 3 and CD = 9

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In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 05 Mar 2014, 07:07
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A
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In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3

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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 05 Mar 2014, 07:26
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kingb wrote:
Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3


Attachment:
Untitled.png
Untitled.png [ 1.73 KiB | Viewed 27448 times ]

First of all notice that triangles CDE and BAE are similar (all three angles there are equal).

This means that the ratio of corresponding sides in these triangles are equal (corresponding sides are opposite equal angles): CD/AB = ED/AE --> 9/3 = ED/AE --> 3 = ED/AE --> 3*AE = ED.

Now, since AD = AE + ED = 4, then AE + 3*AE = 4 --> AE = 1 (and ED = 3).

The area of triangle AEC = 1/2*(base)*(height) = AE*CD = 1/2*1*9 = 4.5.

Answer: D.

Hope it's clear.
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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 05 Sep 2015, 00:50
Made guess that 2<ED<4 according to drawing, so ED=3

Area ACD=18, Area ECD=13.5. So, area AEC=18-13.5=4.5

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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 14 Sep 2015, 12:40
Area of triangle ABC = 6.

6 = 1/2 * b * h where the base is 3, and the height is 4.

Now notice that AEC is more than half of ABC, therefore 4.5 is the answer.
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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 11 Oct 2015, 06:17
Hi Bunuel:

Can you please explain how is the height CD for triangle AEC.
Why is the height of triangle AEC CD??
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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 11 Oct 2015, 06:33
Shree9975 wrote:
Hi Bunuel:

Can you please explain how is the height CD for triangle AEC.
Why is the height of triangle AEC CD??


The altitude/height of a triangle is the perpendicular from the vertex to the opposite side. Note that the side may need to be extended. Thus CD is the height of AEC because CD is the perpendicular from vertex C to the line segment containing the opposite side AE.

Hope it's clear.
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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 21 Feb 2017, 22:49
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kingb wrote:
Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3


Lay Down Foundation: Area of AEC = Area of ABC - Area of ABE

Also, Triangle ABE and CED are similar due to a pair of opposite angles and one right angle in each triangle

So AB/CD = AE/ED
i.e. 3/9 = AE/4-AE
i.e. AE = 1

So, Area of CED = [(1/2)*3*4 - (1/2)*3*1)] = 4.5

Answer: Option D
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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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New post 08 May 2017, 08:44
Calculating the area for triangle ADC b*h/2 = 4*9/2= 18
From there you can eyeball and delete first of all option A. You see that triangle AEC is roughly one-third of triangle ADC, which would be 6.
The only option that comes close to that is option D.
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Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

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Re: In the figure above AD = 4, AB = 3 and CD = 9 &nbs [#permalink] 02 Sep 2018, 09:45
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