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If AD is the same length as DC, what is the area of the parallelogram

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If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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New post 07 Sep 2018, 01:08
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A
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C
D
E

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If AD is the same length as DC, what is the area of the parallelogram shown?


A. \(\frac{25\sqrt{3}}{2}\)

B. 25

C. \(25\sqrt{3}\)

D. \(\frac{75\sqrt{3}}{2}\)

E. \(50\sqrt{3}\)

Attachment:
image023.jpg
image023.jpg [ 4.2 KiB | Viewed 522 times ]

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Re: If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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New post 07 Sep 2018, 02:54
Since the adjacent angles are supplementary. We can calculate the other angles..

If we drop a perpendicular bisector to the diagonal.. we will get 2 triangles following the 30 60 90 rule.

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If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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New post 07 Sep 2018, 10:53
You can find the 2nd diagonal using the formula (side)^2 = (1/2* d1)^2 + (1/2 d2)^2
Then area = 1/2 * d1*d2
Ans E
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If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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New post 08 Sep 2018, 00:11
Using cosine formula of area,

10*10*sin(120)=\(100*\sqrt{3}/2\)=\(50\sqrt{3}\)

Ans. (E)
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Re: If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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New post 09 Sep 2018, 02:18
1
Bunuel wrote:
Image
Note: Figure not drawn to scale

If AD is the same length as DC, what is the area of the parallelogram shown?


A. \(\frac{25\sqrt{3}}{2}\)

B. 25

C. \(25\sqrt{3}\)

D. \(\frac{75\sqrt{3}}{2}\)

E. \(50\sqrt{3}\)

Attachment:
image023.jpg


Since the adjacent sides are equal, opposite angles are parallel and internal angles are not 90, it is a rhombus.
In rhobus, diagonals bisect each other at rt angles.
Suppose diagonals bisect at O.
In triangle OAB, OA=\(5\sqrt{3}\)
OB = 5 as it is a 30-60-90 triangle.
BD=10
Area=1/2* Product of diagonals = \(\frac{1}{2}*10*10\sqrt{3}=50\sqrt{3}\)
Answer E.
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Re: If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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New post 15 Sep 2018, 08:00
how do u know it is a 30-60-90 triangle.
Re: If AD is the same length as DC, what is the area of the parallelogram &nbs [#permalink] 15 Sep 2018, 08:00
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