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Re: In the figure above, lines L and P are parallel. The segment AD is the [#permalink]
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Bunuel wrote:

In the figure above, lines L and P are parallel. The segment AD is the same length as the segment DC; AD is parallel to BC. If the length of AD is equal to 4, and angle ADC is equal to 60º, what is the area of ABCD?

A. 4√2
B. 4√3
C. 8√2
D. 8√3
E. 16√2

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800score Official Solution:

AB is parallel to DC and AD is parallel to BC, so ABCD is parallelogram. We know how to find the area of a parallelogram we multiply the height of parallelogram by its base length.

We are told that the angle ADC is a 60º angle. If we draw an altitude from A straight down and perpendicular to line P, the length of that altitude will be equal to the height of the parallelogram. Moreover, it forms a 60-30-90 triangle, so we can easily find its length. Since the hypotenuse of that triangle is equal to 4, the second longest side must be equal to 2√3 (since the proportions for the triangle run x, x√3, and 2x).

To find the area of a parallelogram , multiply the height of the parallelogram by its base length: 4 × 2√3 = 8√3, or answer choice (D).
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Re: In the figure above, lines L and P are parallel. The segment AD is the [#permalink]
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Re: In the figure above, lines L and P are parallel. The segment AD is the [#permalink]
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