In rectangle ABCD, point E is the midpoint of BC. If the area of quadrilateral ABED is 2/3, what is the area of rectangle ABCD?

(A) 1/2

(B) 3/4

(C) 8/9

(D) 1

(E) 8/3

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Answer:

Choice C
Level of difficulty E M H

Draw yourself a picture as a first step. It will be necessary to realize that in your picture, the line segment ED divides the right half of the rectangle into two equal right triangles. Even though we haven't drawn it, the line segment EA would do the same for the left half of the rectangle. It should be clear at this point that the area of triangle ECD is one fourth the area of the entire rectangle, which we can represent as A, and that quadrilateral ABED is therefore 3/4 of A.

With the given information, we can write that 3/4 * A = 2/3. Multiplying both sides by 4/3 allows us to solve for A, which equals 8/9, or choice C.

For more practice with rectangles, go to Skill Set 12: Geometry - 2D Figures and 3D Solids.

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