# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #8 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?

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The area of the parallelogram can be calculated using the formula:

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

Given that sides A and C form the base of the parallelogram, and the height is the perpendicular distance between them, the height can be found using trigonometry. Since the angle between sides A and C is ( \frac{\pi}{4} ), the height can be calculated as follows:

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

Then, the area can be calculated as:

[ \text{Area} = \text{Length of side A} \times \text{Height} ]

Substituting the given values:

[ \text{Height} = 9 \times \sin\left(\frac{\pi}{4}\right) = 9 \times \frac{\sqrt{2}}{2} = \frac{9\sqrt{2}}{2} ]

[ \text{Area} = 8 \times \frac{9\sqrt{2}}{2} = 36\sqrt{2} ]

So, the area of the parallelogram is ( 36\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.

- 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 # 9 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #48 #, how long are the other two sides?
- A parallelogram has sides with lengths of #16 # and #8 #. If the parallelogram's area is #80 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #2 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #5 #, how long are the other two sides?
- Is an equilateral triangle a quadrilateral?

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