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

Area of parallelogram = 23.182 sq units.

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The area of the parallelogram can be calculated using the formula: Area = base × height. The base of the parallelogram can be taken as side A or side C, and the corresponding height would be the perpendicular distance between these sides. Since sides A and C are adjacent and form an angle, the height can be determined using trigonometry. Specifically, the height can be found using the formula: height = AB * sin(θ), where AB is the length of side B (or side D) and θ is the angle between sides A and C. Once the height is determined, the area can be calculated by multiplying the base by the height.

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

Area = base * height

In a parallelogram, the height is the perpendicular distance between two parallel sides. Given the lengths of sides A, B, C, and D, and the angle between sides A and C, we can find the height using trigonometric principles.

First, let's find the height using the formula for the height of a parallelogram:

Height = side * sin(angle)

We'll use side A as the base and side C as the corresponding height. So, plugging in the values:

Height = 6 * sin((7π)/12)

Now, we need to find the area:

Area = base * height

Area = 6 * (6 * sin((7π)/12))

Area ≈ 6 * (6 * 0.9659)

Area ≈ 6 * 5.794

Area ≈ 34.764 square units

So, the area of the parallelogram is approximately 34.764 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 rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #(7pi)/8 # and the other has a corner with an angle of #(pi)/6 #, what is the difference between the areas of the rhombuses?
- 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?
- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?
- Two opposite sides of a parallelogram each have a length of #8 #. 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?
- A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

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