# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?

The area of the parallelogram is

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To find the area of the parallelogram, you can use the formula:

[ \text{Area} = \text{base} \times \text{height} ]

In a parallelogram, the height is the perpendicular distance between the pair of parallel sides. You can find the height by using trigonometry since you have the length of one side and the angle between the sides.

Given:

- Length of side A (base) = 6
- Angle between sides A and C = ( \frac{3\pi}{8} )

You can find the height using the sine of the given angle:

[ \sin\left(\frac{3\pi}{8}\right) = \frac{\text{height}}{6} ]

Solve for the height:

[ \text{height} = 6 \times \sin\left(\frac{3\pi}{8}\right) ]

Once you have the height, you can calculate the area using the formula mentioned earlier:

[ \text{Area} = 6 \times \text{height} ]

Now, calculate the height and then use it to find the area of the parallelogram.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/4 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #72 #, how long are the other two sides?
- A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #54 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #13 #. If one rhombus has a corner with an angle of #(7pi)/8 # and the other has a corner with an angle of #(pi)/6 #, what is the difference between the areas of the rhombuses?

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