# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?

Area of a parallelogram

Area of a parallelogram

Given

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

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

The base of the parallelogram can be taken as either side ( A ) or side ( C ), and the height is the perpendicular distance between side ( A ) (or ( C )) and side ( D ).

Given that the angle between sides ( A ) and ( C ) is ( \frac{3\pi}{8} ), we can use trigonometric functions to find the height.

[ \text{Height} = |D| \times \sin\left(\frac{3\pi}{8}\right) ]

Substituting the known values, we have:

[ \text{Height} = 2 \times \sin\left(\frac{3\pi}{8}\right) ]

Once you find the height, you can then calculate the area using the formula mentioned earlier.

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