What is the area of the quadrilateral ABCE if BD = 8, AB = 6, and ED = 5? (Note: Figure not drawn to scale.)

A. 10

B. 12

C. 14

D. 16

E. 18

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http://www.800score.com/explanations/GMAT_MATH_T1_Q6_Hard.html(E) Let's break this problem down into steps.

1) To find the area of the quadrilateral ABCE, we are going to subtract the area of triangle AEF from the area of rectangle ABCF. Let's figure out the length of all the sides of triangle AEF and rectangle ABCF.

2) Because BD and AB are 8 and 6, respectively, triangle ABD is a 3-4-5 triangle. AD = 10.

3) If ED = 5 and AD = 10, then AE = 10 – 5, or 5.

4) As alternate angles, angle AEF = angle CED, so triangle AEF must be similar to triangle CED. Because the two triangles are similar and have the same length hypotenuse, the two triangles must be identical.

5) Since AB = EF + EC = 6, and since EF = EC, 2EF = 6. Thus, EF and EC = 3.

6) AF = BC, BC = CD, and BC + CD = BD = 8, so AF, BC, and CD all equal 4.

7) The rectangle ABCF would then have an area = 6 × 4 = 24. The area of a triangle is (base × height)/2. Triangle AEF, therefore, has an area of (4 × 3)/2 = 6.

8) The area of ABCE is 24 – 6 = 18.

The correct answer is choice (E).

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**I don't get how you guys get ED = 5. If AD=10 and AD = ED + AE that's right but we don't know whether the point E is the mid point of the line AD.**