A parallelogram has sides A, B, C, and D. Sides A and B have a length of #1 # and sides C and D have a length of # 6 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?

Answer 1

The area is #~=11.59#

The parallelogram is composed by two equal triangles.

Then you would get the area of each triangle and multiplicate it by 2.

The area of a single triangle is:

#Area_t=A*C*sin hat(AC)#
#=1*6*sin(7pi)/12~=5.8#

Then

#Area_p=2*Area_t~=11.59#
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Answer 2

To find the area of the parallelogram, you can use the formula ( \text{Area} = \text{base} \times \text{height} ). The base can be taken as either side A or side C, and the height is the perpendicular distance between these sides.

Given that sides A and B have a length of 1, and sides C and D have a length of 6, you can take side A as the base. The height of the parallelogram can be found using trigonometry, specifically the sine of the angle between sides A and C.

[ \text{Height} = \text{length of side C} \times \sin\left(\frac{7\pi}{12}\right) ]

[ \text{Height} = 6 \times \sin\left(\frac{7\pi}{12}\right) ]

[ \text{Height} = 6 \times \sin\left(\frac{7\pi}{12}\right) \approx 2.6103 ]

Now, you can calculate the area using the base (side A) and the height:

[ \text{Area} = 1 \times 2.6103 ]

[ \text{Area} \approx 2.6103 ]

So, the area of the parallelogram is approximately 2.6103 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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