Trapezoid

[4meonly]

OA C

[ontopofit]

will go for C.

[4meonly]

The area of the trapezoid = 1/2*(sum of 2 basis)*height

If ABCD is isosceles trapezoid, than x=x and y=y (see picture)
The area of the trapezoid = 1/2*(2(x+y))*height = (x+y)*h
Since we know h=6, we need only (x+y)

(1)
So, We have (x+y)^2 + 6^2 = 10^2
(x+y)^2 = 36
x+y = 6
SUFF

(2)
AB=7, x=7
nothing about y

Answer A

Where is my mistake?

[mridula]

OA C

Let us first drop two perpendiculars from AB to DC, one from point A and one from point B. Let us call the points on DC where the perpendiculars touch P and Q respectively.
Area of the trapezoid is, h(AB+DC)/2.

we know h=6. We need the values of AB and DC to find the value of the Area.


From Statement 1: Since AC = 10, we can say, PC = 8 (Using pythogorus theorem for triangle APC and we know the values for AC and AP as 10 and 6 respectively). But we still don't know the value for DC and AB. So, insuffiecient.


From Statement 2: AB =7. But there is no way to figure out the value of DC. So, insufficient.

Combining statements 1 and 2: Since AB =7. PQ =7. Therefore, QC = (PC-PQ) = (8-1)=7.
QC = DP. Therefore, DP =1.
So, DC = DP+PC = 1+8 = 9.
and we know AB = 7.
So, the area = 6(7+9)/2 = 48.
--- sufficient.

Therefore, i go with C.

[4meonly]

Let us first drop two perpendiculars from AB to DC, one from point A and one from point B. Let us call the points on DC where the perpendiculars touch P and Q respectively.

PD = QC?
I think yes, PD = QC
PD+QC+AB+PQ = 2PD + 2AB

My question is:
PD = QC? If yes, then answer is A

[Vemuri]

The area of the trapezoid = 1/2*(sum of 2 basis)*height

If ABCD is isosceles trapezoid, than x=x and y=y (see picture)
The area of the trapezoid = 1/2*(2(x+y))*height = (x+y)*h
Since we know h=6, we need only (x+y)

(1)
So, We have (x+y)^2 + 6^2 = 10^2
(x+y)^2 = 36
x+y = 6
SUFF

(2)
AB=7, x=7
nothing about y

Answer A

Where is my mistake?

Your assumption that x=x & y=y is not correct. A trapeziod is a quadrilateral that has only 2 sides parallel. It doesn't say anything about the length of the sides.

[4meonly]

What is isosceles trapeziod?

An isosceles trapezoid (isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides (bases) are parallel, the two other sides (legs) are of equal length. The diagonals are of equal length.

https://en.wikipedia.org/wiki/Isosceles_trapezoid
Why my assumption is incorrect?

[Bidisha_800]

I agree with 4meonly. The answer should be (A)

[4meonly]

GMAT Titans, can you comment?

[mals24]

The area of the trapezoid = 1/2*(sum of 2 basis)*height

If ABCD is isosceles trapezoid, than x=x and y=y (see picture)
The area of the trapezoid = 1/2*(2(x+y))*height = (x+y)*h
Since we know h=6, we need only (x+y)

(1)
So, We have (x+y)^2 + 6^2 = 10^2
(x+y)^2 = 36
x+y = 6
SUFF

(2)
AB=7, x=7
nothing about y

Answer A

Where is my mistake?

Ok your reasoning is fine. There is just a small error in the calculation of bold part. x+y = 8. Otherwise your reasoning is correct. Where did you get this question from btw?

[4meonly]

it is from local unofficial source. 10% of OA have mistakes