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Tuck School Moderator
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What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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Updated on: 07 Oct 2018, 03:08
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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:
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Originally posted by LordStark on 06 Oct 2018, 22:21.
Last edited by Bunuel on 07 Oct 2018, 03:08, edited 3 times in total.
Renamed the topic and edited the question.



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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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06 Oct 2018, 23:20
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



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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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06 Oct 2018, 23:24
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 .. Now ED:AD =5:10=1:2 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 ∆ABDarea of ∆DCE=246=18 E
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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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Updated on: 06 Oct 2018, 23:36
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,
CE/AB = DE/AD
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, 23:32.
Last edited by src86 on 06 Oct 2018, 23:36, edited 1 time in total.



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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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06 Oct 2018, 23:35
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 345, 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 Answer (E)
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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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06 Oct 2018, 23:36
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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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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07 Oct 2018, 01:30
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 .. Now ED:AD =5:10=1:2 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 ∆ABDarea of ∆DCE=246=18 E thank you chetan2u sorry for the typo
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Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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07 Oct 2018, 07:24
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 Area of rectangle = width * length = 4*6=24 Area of Right tringle = 3*4*1/2 = 6 Area of quadrilateral = 246 = 18




Re: What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED =
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07 Oct 2018, 07:24






