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Each side of a certain parallelogram has length 6. If the area of the

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Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 26 Jan 2008, 10:31
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Each side of a certain parallelogram has length 6. If the area of the parallelogram is 18. Which of the following is the measure of one of its angles?

A. 30
B. 45
C. 60
D. 90
E. 120
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Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 26 Jan 2008, 10:48
Since it is a PS question, I would pick D on exam.
sides are equal so it most probably a rhomb. if i recall correctly, the area of a rhomb is half the product of its diagonals? d1d2 = 18*2 = 36. perhaps diagonals are equal in lenght (sqrt 36 = 6).

so we have two equilateral traingles. where angles are equal to 60 degrees.
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Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 26 Jan 2008, 11:44
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A

Area=h*a

18=6*h ==> h=3
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Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 26 Jan 2008, 12:50
A too.

We know that Area= base * height. If the Area=18, and base = 6, height must be 3, that is, the angle must be 30º.
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Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 28 Jan 2008, 08:40
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Given each side is 6 and area is 18. We can find the altitude, ie: alt = 18/6 = 3.
Now we have a triangle with one side as 6, the alt as 3, and the base which we don't know.

Using Pythagoras theorem, 6^2 = 3^2 + Base^2 => Base = 3V3
So, the sides are now 3*1, 3*V3, 3*2 => 1:V3:2, which is a 30-60-90 triangle.

Hence the angle that we know is 30, which forms a side of the parallelogram.
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Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 03 Mar 2008, 11:46
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6*6*sin(alpha) = 18 -> sin(alpha) = 1/2 -> alpha = 30 -> A
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Each side of a certain parallelogram has length 6. if the [#permalink] New post 25 Sep 2008, 13:26
Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30’ B. 45’ C. 60’ D. 90’ E.120’

Equal sides of a parallegrame means it's a rhombus -> angle should be either 60 or 120?
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Re: Parallelogram Angels [#permalink] New post 25 Sep 2008, 15:41
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jugolo1 wrote:
Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30’ B. 45’ C. 60’ D. 90’ E.120’

Equal sides of a parallegrame means it's a rhombus -> angle should be either 60 or 120?


Well, you could rule out 60 and 120 right away, because if the parallelogram had an angle of 60 degrees, it would also need to have an angle of 120 degrees (adjacent angles in a parallelogram add to 180), and then there would be two correct answers to the question, which can't happen.

The area of a parallelogram is base*height. The height of this parallelogram must be 3. We therefore need to find the angles in a right angled triangle with a hypotenuse of 6 and a height of 3. That's a 30-60-90, of course, and 30 is the angle opposite the 3, so 30 degrees is one of the angle measures in the parallelogram, and 150 the other.
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Re: Parallelogram Angels [#permalink] New post 26 Sep 2008, 01:10
Ans is 30deg

area of a parallelogram = b*h

b*h=18
h=18/6=3

sin theta =opp/hyp= 3/6

theta = sin inv of 1/2=30 deg
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Re: Parallelogram Angels [#permalink] New post 26 Sep 2008, 09:37
A=b*h or 1/2 d1*d2, if all 4 sides are equal then this is a rhombus, which is basically a tilted square. How can you have a height of 3 and area of 18? Shouldnt height be 6 and area 36? Is this question correctly worded?
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Re: Parallelogram Angels [#permalink] New post 26 Sep 2008, 09:52
bigtreezl wrote:
A=b*h or 1/2 d1*d2, if all 4 sides are equal then this is a rhombus, which is basically a tilted square. How can you have a height of 3 and area of 18? Shouldnt height be 6 and area 36? Is this question correctly worded?


If you have a rhombus with sides b and c, the area will only be b*c if the rhombus is a square. Otherwise the area will be less than b*c. To find the area of a rhombus (or any other parallelogram), you need to multiply the base and the height. If your parallelogram is 'tilted' (i.e. if the angles are not all 90 degrees), then the height is definitely not one of the sides. In this example, the rhombus is pretty seriously tilted to get an area as small as 18.
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Re: Parallelogram Angels [#permalink] New post 26 Sep 2008, 10:18
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Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink] New post 11 Oct 2014, 04:24
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Re: Each side of a certain parallelogram has length 6. If the area of the   [#permalink] 11 Oct 2014, 04:24
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