A parallelogram has sides A, B, C, and D. Sides A and B have a length of #7 # and sides C and D have a length of # 6 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?

Answer 1

#38.803 " square units"#

Refer to the figure below

A and B are the parallel sides with the same length, 7. C and D are also parallel sides with the same length, 6. #alpha=(3pi)/8 radians=67.5^@.#

Side C meets side A, forming angle alpha. If we draw a line from the other endpoint of side C, a line that is perpendicular to side A, the obtained segment is the height (#"h"#) relatively to side A. As we can see from the figure:
#sin alpha="opposed cathetus"/"hypotenuse"#
#sin 67.5^@=h/C# => #h=6*sin 67.5^@~=5.543#

Since the area of a parallelogram is given by
#A=base xx height#
#A=7*6*sin 67.5^@~=38.803#

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Answer 2

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

[ \text{Area} = \text{Base} \times \text{Height} ]

where the base is the length of one of the sides (let's say ( A )), and the height is the perpendicular distance between side ( A ) and side ( C ).

To find the height, use trigonometry. Since the angle between sides ( A ) and ( C ) is given as ( \frac{3\pi}{8} ), you can use the sine of this angle to find the height.

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

Now, substitute the given values:

[ \text{Height} = 7 \times \sin\left(\frac{3\pi}{8}\right) ]

Then, multiply the base by the height to find the area.

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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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