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

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Math Expert
Joined: 02 Sep 2009
Posts: 53060
If AD is the same length as DC, what is the area of the parallelogram  [#permalink]

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07 Sep 2018, 00:08
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:25) correct 21% (02:56) wrong based on 51 sessions

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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 [ 4.2 KiB | Viewed 826 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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07 Sep 2018, 01:54
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.

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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07 Sep 2018, 09:53
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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07 Sep 2018, 23:11
1
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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09 Sep 2018, 01:18
1
Bunuel wrote:

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 = $$\frac{1}{2}*10*10\sqrt{3}=50\sqrt{3}$$
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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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15 Sep 2018, 07:00
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   [#permalink] 15 Sep 2018, 07:00
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