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?

Answer 1

Area of parallelogram is #18.478# units.

Area of a parallelogram is given by #axxbxxsintheta#, where #a# is length of one pair of equal sides and #b# is the length of other pair of sides of a parallelogram and #theta# is the angle between them.
As one pair of sides is #5#, other two are #4# units long and included angle is #sin(5pi/8)#
Area of parallelogram is given by #5xx4xxsin(5pi/8)#
or #20xx0.9239=18.478#
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Answer 2

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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Answer from HIX Tutor

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.

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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