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?
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. 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 ( Since the area of a parallelogram is given by
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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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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.
- Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #81 #, how long are the other two sides?
- 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 # 5 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?
- A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #18 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #96 #, how long are the other two sides?

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