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605-655 (Medium)|   Geometry|      
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MathRevolution
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 07 Mar 2016, 16:55
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

71% (02:45) correct 29% (03:01) wrong based on 167 sessions

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Attachment:
trapezoid ABCD.jpg
trapezoid ABCD.jpg [ 4.86 KiB | Viewed 5681 times ]
If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7


* A solution will be posted in two days.
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C
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 09 Mar 2016, 03:07
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If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7


* A solution will be posted in two days.
Show more

HI..
Although it should be given that O is the center, I take it as center..

Join AO.. we have an isosceles triangle with equal sides as radius or 4 and the third side as 6
so throw an altitude on AB from O as shown..

the ALTITUDE= \(\sqrt{4^2-3^2}=[m]\sqrt{7}\)[/m]..
now we know two side as 6 and 8 and ALTITUDE as \(\sqrt{7}\)..
Area= \(\frac{(6+8)}{2}*\sqrt{7}\)=\(7\sqrt{7}\)

C
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 11 Mar 2016, 05:51
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If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7

->Since AB=6, HC=1 and OH=3. Then, BH=√(4^2-3^2 )=√7. So, the area of the trapezoid ABCD is (1/2)(6+8)√7=7√7.
Thus, C is the answer.
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 27 Mar 2016, 06:14
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chetan2u
MathRevolution
Attachment:
trapezoid ABCD.jpg
If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7


* A solution will be posted in two days.

HI..
Although it should be given that O is the center, I take it as center..

Join AO.. we have an isosceles triangle with equal sides as radius or 4 and the third side as 6
so throw an altitude on AB from O as shown..

the ALTITUDE= \(\sqrt{4^2-3^2}=[m]\sqrt{7}\)[/m]..
now we know two side as 6 and 8 and ALTITUDE as \(\sqrt{7}\)..
Area= \(\frac{(6+8)}{2}*\sqrt{7}\)=\(7\sqrt{7}\)

C
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How can we assume that the altitude from O to AB will bisect AB?
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aekukula
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 27 Mar 2016, 06:28
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MathRevolution
If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7

->Since AB=6, HC=1 and OH=3. Then, BH=√(4^2-3^2 )=√7. So, the area of the trapezoid ABCD is (1/2)(6+8)√7=7√7.
Thus, C is the answer.
Show more

hold up... where did u get HC = 1 and OH = 3 from ?
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 27 Mar 2016, 23:26
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aekukula
MathRevolution
If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7

->Since AB=6, HC=1 and OH=3. Then, BH=√(4^2-3^2 )=√7. So, the area of the trapezoid ABCD is (1/2)(6+8)√7=7√7.
Thus, C is the answer.

hold up... where did u get HC = 1 and OH = 3 from ?
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From A, draw a line downwards vertically and it makes a point. Suppose the point E, which makes AB=EH=6. Then, (8-6)/2=HC=DE and OH=4-HC=4-1=3.
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 03 Apr 2016, 18:38
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two things i really wanna mention here
First =>This is a very poor Quality GMAT Question .
And i myself being a very poor GMAT question writer can actually say that.. :)

The Golden Rule of Gmat => """ IT THEY DO NOT SAY => NEVER EVER EVER ASSUME """
So O may or may not be the centre of the circle ..

Regards...
S.C.S.A

P.S => I actually solved this question for 15 minutes without taking O as the centre.. :)
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 03 Apr 2016, 18:38
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MeghaP
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MathRevolution
Attachment:
trapezoid ABCD.jpg
If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7


* A solution will be posted in two days.

HI..
Although it should be given that O is the center, I take it as center..

Join AO.. we have an isosceles triangle with equal sides as radius or 4 and the third side as 6
so throw an altitude on AB from O as shown..

the ALTITUDE= \(\sqrt{4^2-3^2}=[m]\sqrt{7}\)[/m]..
now we know two side as 6 and 8 and ALTITUDE as \(\sqrt{7}\)..
Area= \(\frac{(6+8)}{2}*\sqrt{7}\)=\(7\sqrt{7}\)

C

How can we assume that the altitude from O to AB will bisect AB?
Show more


Hey MeghaP the reason here is => The perpendicular drawn from the centre of the circle to the chord => Always Bisects the chord..
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 04 Apr 2016, 01:27
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If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7


* A solution will be posted in two days.

HI..
Although it should be given that O is the center, I take it as center..

Join AO.. we have an isosceles triangle with equal sides as radius or 4 and the third side as 6
so throw an altitude on AB from O as shown..

the ALTITUDE= \(\sqrt{4^2-3^2}=[m]\sqrt{7}\)[/m]..
now we know two side as 6 and 8 and ALTITUDE as \(\sqrt{7}\)..
Area= \(\frac{(6+8)}{2}*\sqrt{7}\)=\(7\sqrt{7}\)

C

How can we assume that the altitude from O to AB will bisect AB?
Show more


Hey MeghaP the reason here is => The perpendicular drawn from the centre of the circle to the chord => Always Bisects the chord..[/quote]


Thank you so much for this :)
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 12 Jun 2017, 07:59
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this question has to mention O is a center of a circle
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 22 Mar 2021, 12:03
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MathRevolution
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If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7

->Since AB=6, HC=1 and OH=3. Then, BH=√(4^2-3^2 )=√7. So, the area of the trapezoid ABCD is (1/2)(6+8)√7=7√7.
Thus, C is the answer.

hold up... where did u get HC = 1 and OH = 3 from ?


From A, draw a line downwards vertically and it makes a point. Suppose the point E, which makes AB=EH=6. Then, (8-6)/2=HC=DE and OH=4-HC=4-1=3.
Show more

Casting the issue about O being the centre of the circle aside...

I am still confused how HC = 1 and OH = 3

The way I interpreted it was the base of both triangles is 1. Hence, if we take the altitude as bisecting the base, then each of two right triangles have a base of 0.5. The hypotenuse is 4.

4^2 = 0.5^2 + x^2 ...solve for x to get the height.

What did I miss?
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If AB=6, DC=8, what is the area of the trapezoid ABCD? 03 Apr 2021, 18:56
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aekukula
MathRevolution
If AB=6, DC=8, what is the area of the trapezoid ABCD?

A. √7
B. 7
C. 7√7
D. 5√7
E. 6√7

->Since AB=6, HC=1 and OH=3. Then, BH=√(4^2-3^2 )=√7. So, the area of the trapezoid ABCD is (1/2)(6+8)√7=7√7.
Thus, C is the answer.

hold up... where did u get HC = 1 and OH = 3 from ?
Show more





can someone explain the derivation of root7 clearly?
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