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A parallelogram has sides A, B, C, and D. Sides A and B have a length of #3 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?

Answer 1

Claire Akin

Area of parallelogram is #16.9704#

If #a# and #b# are sides of a parallelogram and included angle is #theta#,

then area of the parallelogram is given by #axxbxxsintheta#

As #a=3#, #b=8# and #theta=(3pi)/4#

Area of parallelogram is

#3xx8xxsin(3pi)/4=24xx1/sqrt2=12xxsqrt2=12xx1.4142=16.9704#

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Answer 2

Avery Allen

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

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

In this case, we can take side ( A ) as the base and find the height by projecting side ( C ) onto ( A ) using trigonometry.

The height ( h ) is given by:

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

Where ( \theta = \frac{3\pi}{4} ).

After finding the height, we can calculate the area using the formula mentioned above.

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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.