# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 1 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?

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The area of the parallelogram can be calculated using the formula: Area = base * height. In this case, the base is the length of side A, which is 2 units, and the height is the perpendicular distance between side A and side C. To find the height, we can use trigonometry.

Since the angle between sides A and C is given as (3π)/8, we can use the sine function to find the height:

sin((3π)/8) = height / 1

Solving for height:

height = sin((3π)/8) * 1

Now, we can calculate the area using the formula:

Area = base * height

Area = 2 * sin((3π)/8) * 1

Area ≈ 1.329 square units.

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The area of the parallelogram is ( A = 2 \sin(\theta) ), where ( \theta ) is the angle between sides A and C. Given ( \theta = \frac{3\pi}{8} ), the area can be calculated as ( A = 2 \sin\left(\frac{3\pi}{8}\right) ).

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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 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 #81 #, how long are the other two sides?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #7 # and sides C and D have a length of # 5 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?
- A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #18 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #96 #, how long are the other two sides?

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