# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #(5 pi)/8 #, what is the area of the parallelogram?

Area of parallelogram is 13.858

Area of a parallelogram

Given length = l = 5, width = w = 3 and

Area of parallelogram = A = l * h = 5 * 2.7716 = 13.858#

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

Area = base × height

The base of the parallelogram can be any of its sides. Since the given sides are labeled as A, B, C, and D, let's consider sides A and B as the base. The height of the parallelogram is the perpendicular distance between the base and the opposite side.

First, we need to find the height. We can use trigonometry to find the height. Considering the given angle between sides A and C, we can find the height using the sine function:

sin(θ) = opposite / hypotenuse

Here, θ = (5π)/8 and the opposite side is the height (h), and the hypotenuse is side A (5).

sin((5π)/8) = h / 5

Solving for h, we get:

h = 5 * sin((5π)/8)

Now, we have the height. To find the area, we multiply the base (5) by the height (h):

Area = 5 * h

Substitute the value of h:

Area = 5 * (5 * sin((5π)/8))

Calculate sin((5π)/8):

sin((5π)/8) ≈ 0.9239

Area ≈ 5 * (5 * 0.9239)

Area ≈ 23.0975

So, the area of the parallelogram is approximately 23.0975 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.

- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #66 #, what is the length of its longest diagonal?
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- Two opposite sides of a parallelogram have lengths of #7 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #42 #, how long are the other two sides?
- A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?
- A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions?

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