# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?

The area is

Using the pythagorean theorem, we can see that, if K, L, M the sides of the right triangle (M is the hypotenuse, and K = L),

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To find the area of the parallelogram, you can use the formula: Area = base × height. Since the height of a parallelogram is the perpendicular distance between the parallel sides, you can find it using trigonometry.

First, find the height of the parallelogram by taking the sine of the angle between sides A and C, which is π/4:

sin(π/4) = height / length of side C

Then, rearrange the equation to solve for the height:

height = length of side C × sin(π/4)

Next, calculate the area using the formula:

Area = length of side A × height

Substitute the given values into the formulas:

height = 9 × sin(π/4)

Now, calculate the height:

height = 9 × sin(π/4) = 9 × (1/√2) = 9√2 / 2

Now that you have the height, substitute it into the formula for the area:

Area = 2 × (9√2 / 2)

Simplify:

Area = 9√2

So, the area of the parallelogram is 9√2 square units.

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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.

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