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In the figure, ABCD and ABEC are parallelograms. The area of

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In the figure, ABCD and ABEC are parallelograms. The area of [#permalink] New post 24 Mar 2019, 00:12
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In the figure, ABCD and ABEC are parallelograms. The area of the quadrilateral ABED is 6. What is the area of the parallelogram ABCD ?

(A) 2

(B) 4

(C) 4.5

(D) 5

(E) 6
[Reveal] Spoiler: OA

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Re: In the figure, ABCD and ABEC are parallelograms. The area of [#permalink] New post 10 Sep 2019, 00:02
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We can observe that AB = DC = CE (opposite sides of a parallelogram are equal) let us take that value as x.

Now, the area of a trapezoid is 0.5*(d1 + d2)* h, where d1 and d2 are the parallel sides and h is the height. Therefore, the area of ABED = 6 = 0.5(x + 2x) * h.
Simplifying the equation, we get 3*x*h = 12, which means x*h = 4, which is the area of the parallelogram. Therefore, the answer is B
Re: In the figure, ABCD and ABEC are parallelograms. The area of   [#permalink] 10 Sep 2019, 00:02
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In the figure, ABCD and ABEC are parallelograms. The area of

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