# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #3 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(5 pi)/8 #, what is the area of the parallelogram?

The area is

The area of a parallelogram equals the product of the two nonparallel sides times the some of the angle at the vertex where the two sides meet. Since all vertex angles are either congruent or supplementary to each other the sine value is always the same.

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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 the parallelogram represent the base and the height, we need to find the length of the height.

The height of the parallelogram is the perpendicular distance between side (A) and side (C). To find this height, we can use trigonometry, specifically the sine function.

The height ((h)) can be found using the formula (h = |AC| \sin(\theta)), where (|AC|) is the length of side (C), and (\theta) is the angle between sides (A) and (C).

Given that (|AC| = 8) and (\theta = \frac{5\pi}{8}), we can calculate the height.

[ h = 8 \sin\left(\frac{5\pi}{8}\right) ]

Next, we can use the formula for the area of a parallelogram:

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

[ \text{Area} = 3 \times 8 \sin\left(\frac{5\pi}{8}\right) ]

[ \text{Area} = 24 \sin\left(\frac{5\pi}{8}\right) ]

Thus, the area of the parallelogram is ( 24 \sin\left(\frac{5\pi}{8}\right) ).

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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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- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #81 #, what is the length of its longest diagonal?
- What is a quadrilateral with one right angle?
- Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #(7pi)/8 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?
- Find the equation of a line passing through #(1,1/2)# and making an angle #pi/6# to the line #y=1/2x#?

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