# 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 # 4 #. If the angle between sides A and C is #(5 pi)/8 #, what is the area of the parallelogram?

Area of parallelogram is

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To find the area ( A ) of a parallelogram given the lengths of two adjacent sides ( A ) and ( C ) and the angle ( \theta ) between them, you can use the formula:

[ A = A \times C \times \sin(\theta) ]

Given: ( A = 5 ) ( C = 4 ) ( \theta = \frac{5\pi}{8} )

Plug in the given values:

[ A = 5 \times 4 \times \sin\left(\frac{5\pi}{8}\right) ]

Using a calculator to find the sine of ( \frac{5\pi}{8} ):

[ \sin\left(\frac{5\pi}{8}\right) \approx 0.9239 ]

Now, substitute this value into the formula:

[ A = 5 \times 4 \times 0.9239 ] [ A = 20 \times 0.9239 ] [ A = 18.478 ]

So, the area of the parallelogram is approximately ( 18.478 ) 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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- Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

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