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# What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =

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Manager
Joined: 31 Aug 2016
Posts: 168
Location: India
Concentration: Finance, General Management
GMAT 1: 680 Q49 V33
GMAT 2: 700 Q49 V37
GPA: 2.81
What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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Updated on: 07 Oct 2018, 02:08
1
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:21) correct 29% (02:52) wrong based on 35 sessions

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What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED = 5? (Note: Figure not drawn to scale.)

A. 10
B. 12
C. 14
D. 16
E. 18

Source:800 score

Attachment:

img1.jpg [ 4.08 KiB | Viewed 509 times ]

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Originally posted by PeepalTree on 06 Oct 2018, 21:21.
Last edited by Bunuel on 07 Oct 2018, 02:08, edited 3 times in total.
Renamed the topic and edited the question.
Intern
Joined: 14 Jul 2016
Posts: 8
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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06 Oct 2018, 22:20
Hi,
Are you sure the question is asking for the area of the quadrilateral ABCD ? Because it is not making any sense from the given diagram ? Correct me if I my understanding is wrong.

//Sayan
Math Expert
Joined: 02 Aug 2009
Posts: 7100
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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06 Oct 2018, 22:24
1
2
PeepalTree wrote:
What is the area of the quadrilateral ABCD if BD=8, AB=6, and ED=5?

a. 10
b. 12
c. 14
d. 16
e. 18

Source:800 score

I am sure PeepalTree, you mean ABCE and not ABCD..
Now let's solve step wise..

Step I....
Take ∆ABD, a right angled triangle with sides in ratio 3:4:5 so AD = 2*5=10 or
$$AD^2=AB^2+BD^2=6^2+8^2=10^2......AD=10$$
Step II....
Take ∆s ABD and DEC..
AB and CE are perpendicular on BD..
So ABD and DEC are similar ..
So areas will be in ratio 1^2:2^2=1:4
Step III....
Now area of ∆ABD is AB*BD*1/2=8*6/2=24
Area of ∆DEC is 24*1/4=6.. rule of ratios of similar triangles
Area of quadrilateral / trapezium ABCE is area of ∆ABD-area of ∆DCE=24-6=18

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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Updated on: 06 Oct 2018, 22:36
Hi Chetan,
From Triangle ABD, AE = 5.
And since opp. angles in the quadrilateral are 90 degree each, I took AB=FC = 6 and E as the mid pt. (based on the figure). Is this incorrect approach ?

Also I figured Triangle ABD and DEC are similar,

Therefore CE =3 and it satisfies the mid pt. assumption.

Area of Quadrilateral ABCF = 6x4 =24 sq. units. and area of Triangle AEF = 6 sq. units.

Therefore, area of quad. ABCE = 24 -6 = 18 (E)

Originally posted by src86 on 06 Oct 2018, 22:32.
Last edited by src86 on 06 Oct 2018, 22:36, edited 1 time in total.
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Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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06 Oct 2018, 22:35
2
PeepalTree wrote:
What is the area of the quadrilateral ABCE if BD=8, AB=6, and ED=5?

a. 10
b. 12
c. 14
d. 16
e. 18

Source:800 score

Assuming we are looking for area of quad ABCE,

Triangle ABD is right angled. AB = 6 and BD = 8 so using multiple of pythagorean triplet 3-4-5, AD = 10

Triangles ABD and ECD are similar by AA (both have a common angle D and 90 degree angles)
So
$$\frac{Area ECD}{Area ABD} = (\frac{ED}{AD})^2 = \frac{1}{4}$$

Area ABCE = (3/4)*Area of triangle ABD = (3/4) * (1/2) * 6 * 8 = 18

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Joined: 02 Aug 2009
Posts: 7100
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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06 Oct 2018, 22:36
1
src86 wrote:
Hi Chetan,
From Triangle ABD, AE = 5.
And since opp. angles in the quadrilateral are 90 degree each, I took AB=FC = 6 and E as the mid pt. (based on the figure). Is this incorrect approach ?

Area of Quadrilateral ABCF = 6x4 =24 sq. units. and area of Triangle AEF = 6 sq. units.

Therefore, area of quad. ABCE = 24 -6 = 18 (E)

No, you cannot take E as the midpoint unless it is clearly specified or you prove and then work ahead.
But a big NO to taking these estimates from the figures
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Manager
Joined: 31 Aug 2016
Posts: 168
Location: India
Concentration: Finance, General Management
GMAT 1: 680 Q49 V33
GMAT 2: 700 Q49 V37
GPA: 2.81
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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07 Oct 2018, 00:30
chetan2u wrote:
PeepalTree wrote:
What is the area of the quadrilateral ABCD if BD=8, AB=6, and ED=5?

a. 10
b. 12
c. 14
d. 16
e. 18

Source:800 score

I am sure PeepalTree, you mean ABCE and not ABCD..
Now let's solve step wise..

Step I....
Take ∆ABD, a right angled triangle with sides in ratio 3:4:5 so AD = 2*5=10 or
$$AD^2=AB^2+BD^2=6^2+8^2=10^2......AD=10$$
Step II....
Take ∆s ABD and DEC..
AB and CE are perpendicular on BD..
So ABD and DEC are similar ..
So areas will be in ratio 1^2:2^2=1:4
Step III....
Now area of ∆ABD is AB*BD*1/2=8*6/2=24
Area of ∆DEC is 24*1/4=6.. rule of ratios of similar triangles
Area of quadrilateral / trapezium ABCE is area of ∆ABD-area of ∆DCE=24-6=18

E

thank you chetan2u sorry for the typo
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Joined: 09 Mar 2016
Posts: 1208
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =  [#permalink]

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07 Oct 2018, 06:24
PeepalTree wrote:

What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED = 5? (Note: Figure not drawn to scale.)

A. 10
B. 12
C. 14
D. 16
E. 18

Source:800 score

Attachment:
img1.jpg

Area of rectangle = width * length = 4*6=24

Area of Right tringle = 3*4*1/2 = 6

Area of quadrilateral = 24-6 = 18
Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED = &nbs [#permalink] 07 Oct 2018, 06:24
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