# 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 # 3 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?

The area of the parallelogram is

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The area of the parallelogram is ( 2 \times 3 \times \sin\left(\frac{7\pi}{18}\right) ), which equals approximately ( 3.66 ).

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

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

Since the sides of a parallelogram are parallel, the height of the parallelogram can be found by dropping a perpendicular from one side to the opposite side.

In this case, we'll consider side A as the base and side C as the height.

The area of the parallelogram is given by:

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

[ \text{Area} = 2 \times 3 \times \sin\left(\frac{7\pi}{18}\right) ]

[ \text{Area} = 6 \times \sin\left(\frac{7\pi}{18}\right) ]

[ \text{Area} = 6 \times \sin\left(\frac{7\pi}{18}\right) ]

[ \text{Area} \approx 3.0917 ]

So, the area of the parallelogram is approximately 3.0917 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 with lengths of #15 # and #12 #. If the parallelogram's area is #54 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(11pi)/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- It is given that line MO = line TR and line NP = line QS, where MNOP and TQRS are parallelograms. A student has said that if those statements are true, then MNOP = TQRS. Why is this student incorrect?
- 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 #36 #, how long are the other two sides?

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