# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #1 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?

area of given parallelogram is

area of given parallelogram is

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The area of a parallelogram is given by the formula:

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

In this case, the base of the parallelogram is the length of side (C), which is 2 units. To find the height, we can use the sine of the angle between sides (A) and (C), which is (\frac{3\pi}{4}) radians. The height is given by:

[ \text{Height} = \text{side} \times \sin(\text{angle}) ]

Substitute the values:

[ \text{Height} = 1 \times \sin\left(\frac{3\pi}{4}\right) ]

[ \text{Height} = 1 \times \frac{\sqrt{2}}{2} ]

[ \text{Height} = \frac{\sqrt{2}}{2} ]

Now, we can calculate the area:

[ \text{Area} = 2 \times \frac{\sqrt{2}}{2} ]

[ \text{Area} = \sqrt{2} ]

So, the area of the parallelogram is (\sqrt{2}) square units.

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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 #4 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #32 #, how long are the other two sides?
- Two opposite sides of a parallelogram have lengths of #8 #. If one corner of the parallelogram has an angle of #pi/8 # and the parallelogram's area is #15 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #14 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #70 #, how long are the other two sides?
- A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?
- For quadrilateral ABCD, the coordinates of vertices A and B are A(1,2) and B(2,-2). Match each set of coordinates for vertices C and D, that is the most specific way to classify the quadrilateral.?

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