ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p

Question

https://gmatclub.com/forum/download/file.php?id=27110 ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a point between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD? (Note: figure not drawn to scale.) A. 30 inches B. 35 inches C. 40 inches D. 45 inches E. 50 inches Kudos for a correct solution . 2015-07-01_1359.png

chetan2u · Answer

lets see the area first .. AE is 5 inches long, and the area of triangle AED is 12.5 square inches.. (1/2)*5*DE=12.5
so DE=5.. as E is the mid point CD=10..
now AB ll CD ..
so it is a trapezium with LLel sides 10 and 4 with height 5..
area of ABCD =(10+4)*5/2=35..
ans B

GMATinsight · Answer

Draw the figure for every geometry question

Answer: Option B

balamoon · Answer

Solution -

Area of AED = 1/2(DE*AE) -> 12.5 = 0.5 (DE*5) -> DE = 5.
E is the mid point, so DE = EC =5.

Area of quadrilateral ABCD = 1/2(DC+AB)*AE = 0.5*(10+4)*5 =   35 inches^2 .

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

If E is the midpoint of C, then CE = DE = x. You can determine the length of x by using what you know about the area of triangle AED:

A = (b*h)/2;
12.5 = 5x/2;
x = 5.

Therefore, the length of CD is 2x, or 10.

To find the area of the trapezoid, use the formula:
 A=\frac{b_1+b_2}{2}*h=\frac{4+10}{2}*5=35  in^2.

Answer: B.

asfandkhan · Answer

Hello,

I tried solving the problem in a slightly different way and ended up getting a different answer. There is obviously a gap in my understanding so would really appreciate if someone could point that out. Here was my thought process:

Since AB=4 and CE=AB, where is E is the midpoint of CD, wouldn't CD=2AB or 2CE or 2*4=8?

Area= (4+8)*5/2=30

Thanks again,
Asfand

tittoo · Answer

If we are not given that E is a midpoint, how can we solve this via decomposition?
I tried solving for the area of the triangle on the left, the rectangle in the middle but got stuck with the area of the triangle on the right.

How to solve for the area of the triangle on the right?
I have the height as 5 but not the base.

Thanks!

bumpbot · Answer

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ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p

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ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p

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