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Trapezoid

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by vinay1983 » Sun Oct 06, 2013 8:38 am
If ABCD is a trapezoid, where AB is parallel to CD, what is the area of ABCD?

(1) 2(AB) + CD = 12

(2) The height of the trapezoid is 5 inches
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Source: — Data Sufficiency |

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Trapezoid

by Brent@GMATPrepNow » Sun Oct 06, 2013 9:37 am
vinay1983 wrote: Image
If ABCD is a trapezoid, where AB is parallel to CD, what is the area of ABCD?

(1) 2(AB) + CD = 12

(2) The height of the trapezoid is 5 inches
The area of the trapezoid is (average of the 2 "bases")(height)
In other words, area = [(AB+CD)/2][height]

Here are 2 trapezoids that satisfy the conditions in statements 1 and 2 combined.

Trapezoid A
Image
Here, the area = 25

Trapezoid B
Image
Here, the area = 22.5

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 2:09 pm, edited 1 time in total.
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by TheGmatTutor » Tue Oct 08, 2013 8:48 am
The formula for the area of a trapezoid is (1/2)*(base1 + base2)*height. In other words, it's the average of the two bases times the height. In this problem, it would be

Area = (1/2)*(AB+CD)*height

S1. Does not tell you anything about the height; insufficient
S2. Does not tell you anything about the bases; insufficient

Together, you know that 2AB+CD = 12 and the height is 5; however, you don't know the average of the two bases AB and CD.

Answer: E
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