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605-655 (Medium)|   Geometry|      
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Bunuel
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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area 20 Oct 2021, 03:00
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71% (02:08) correct 29% (01:59) wrong based on 175 sessions

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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area of the trapezoid?

(1) Angle ADE is 60 degrees.

(2) AD is parallel to BC.


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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area 03 Nov 2021, 06:43
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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area 11 Dec 2021, 11:38
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Below Information is mentioned in the question : ED = 5 and AB = 12

Statement 1 : Angle ADE is 60 degrees.
Using this information we can get length of side AE and AD and we can found are for the triangle AED. But area for ABCD is still unknown. Not Sufficient

Statement 2 : AD is parallel to BC.
Since AB and CE are parallel. But length of side AD or BC is still unknown. Not Sufficient.

Statement 1 + Statement 2 : Using both statement we can find the area for triangle AED (1/2 * AE*ED) and the area for ABCD using (AB or CD) and (AD or BC). Sufficient

Ans : C
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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area 13 Dec 2021, 08:31
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Bunuel

Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area of the trapezoid?

(1) Angle ADE is 60 degrees.

(2) AD is parallel to BC.



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From statement 1, we can find the value of AE which will be 5\sqrt{3}
From statement 2, we know that CD is equal to AB. CE = CD+DE = 17

Area of the trapezoid can be found out if we know the length of 2 parallel sides and the distance between them

Option C
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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area 21 Dec 2021, 03:42
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Area of trapezoid ABCE = 1/2 * AE * (AB + EC)

(1) Angle ADE is 60 degrees.
---> AD = 2 * ED = 12.
---> AE = √108.
---> Unable to calculate EC.
---> The area cannot be calculated.
=> Not enough.

(2) AD is parallel to BC.
---> ABCD is a parallelogram.
---> DC = AB = 12. ---> EC = 17.
---> Cannot calculate AE.
---> The area cannot be calculated.
=> Not enough.

(1) + (2) ---> AE = √108, EC = 17 and AB = 12.
---> Calculate the area.
=> Enough.

Answer: C.
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Figure ABCE is a trapezoid with ED = 5 and AB = 12. What is the area 27 Dec 2022, 22:09
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Given information

ABCE is a trapezoid
AB=12,ED=5

1) In Triangle AED
Angle ADE = 60, Therefore angle EAD = 30
Therefore sides ED:AE:AD is in the ratio 1:1.732:2

Therefore side AE = 5*1.732=8.67
Therefore area of triangle = 1/2* ED*AE=1/2*5*8.67=21.68
Area of the figure ABCD is not given and the given information is Insufficient to find the area

2) AD\\BC
Therefore area of the parallelogram ABCD is equal to AE*AB = 8.67*12=104.04
In the trapezium ABCE area of the triangle AED is not known.

Therefore statement 2 alone is insufficient to find the correct answer

Option C - statement 1+2 that is area of trapezium ABCE=Area of triangle AED+ Area of \\ ABCD=21.68+104.04

Sufficient

IMO C
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