# 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 # 2 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?

The area of 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} ]

For a parallelogram, any side can be considered the base, and the height is the perpendicular distance between the base and its opposite side.

Given that sides (A) and (C) form the base and the angle between them is (\frac{3\pi}{4}), you can use trigonometric principles to find the height.

First, find the height using the sine of the angle between sides (A) and (C):

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

Substitute the values:

[ \text{Height} = 2 \times \sin\left(\frac{3\pi}{4}\right) ]

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

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

Now, you have the base ((A)) and the height of the parallelogram. Plug these values into the formula for the area:

[ \text{Area} = 6 \times \sqrt{2} ]

[ \text{Area} = 6\sqrt{2} ]

So, the area of the parallelogram is (6\sqrt{2}).

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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.

- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #4 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #32 #, how long are the other two sides?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #180 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #120 #, what is the length of its longest diagonal?
- In the parallelogram find: the value of x, total perimeter and area of DEIK?

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