# 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 # 6 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?

The area is

The parallelogram is composed by two equal triangles.

Then you would get the area of each triangle and multiplicate it by 2.

The area of a single triangle is:

Then

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To find the area of the parallelogram, you can use the formula ( \text{Area} = \text{base} \times \text{height} ). The base can be taken as either side A or side C, and the height is the perpendicular distance between these sides.

Given that sides A and B have a length of 1, and sides C and D have a length of 6, you can take side A as the base. The height of the parallelogram can be found using trigonometry, specifically the sine of the angle between sides A and C.

[ \text{Height} = \text{length of side C} \times \sin\left(\frac{7\pi}{12}\right) ]

[ \text{Height} = 6 \times \sin\left(\frac{7\pi}{12}\right) ]

[ \text{Height} = 6 \times \sin\left(\frac{7\pi}{12}\right) \approx 2.6103 ]

Now, you can calculate the area using the base (side A) and the height:

[ \text{Area} = 1 \times 2.6103 ]

[ \text{Area} \approx 2.6103 ]

So, the area of the parallelogram is approximately 2.6103 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.

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