A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?

Answer 1

Area of the parallelogram is #17.39(2dp)# sq.unit

We know the area of the parallelogram as #A_p=s_1*s_2*sin theta.# Here #s_1=6 ; s_2=3; theta= (7*180)/12=105^0 or (180-105)=75^0# Therefore, Area #A_p= 6*3*sin75=17.39 (2dp)#
Area of the parallelogram is #17.39(2dp)# sq.unit [Ans]
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Answer 2

The area of the parallelogram can be calculated using the formula:

[ \text{Area} = \text{base} \times \text{height} ]

Where the base is one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.

In this case, we can take side A as the base and find the height. To find the height, we can use trigonometry since we have the angle between sides A and C.

The height (h) can be calculated as:

[ h = AC \times \sin(\theta) ]

Where AC is the side length and ( \theta ) is the angle between sides A and C.

Given that side A has a length of 6 and side C has a length of 3, we can find the length of AC using the cosine rule:

[ AC^2 = A^2 + C^2 - 2AC \cdot A \cdot C \cdot \cos(\theta) ]

Finally, the area of the parallelogram is:

[ \text{Area} = 6 \times h ]

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Answer 3

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

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

In a parallelogram, any side can be considered as the base, and the corresponding height is the perpendicular distance between the base and the opposite side.

Given that sides A and B have a length of 6, and sides C and D have a length of 3, and the angle between sides A and C is ( \frac{7\pi}{12} ), we can use trigonometry to find the height of the parallelogram.

We'll focus on side A as the base. The height of the parallelogram can be found by using the sine of the angle between sides A and C, since the height forms the opposite side of this angle.

Using the sine formula:

[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} ]

we can solve for the height:

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

Given that side C has a length of 3, and using the value of sine ( \sin\left(\frac{7\pi}{12}\right) ), we can calculate the height.

Once we have the height, we can then find the area of the parallelogram using the formula:

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

Substitute the values of the base and height into this formula to get the area of the parallelogram.

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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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