# Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?

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To find the difference between the areas of the rhombuses, we first need to calculate the areas of each rhombus separately and then find the difference.

The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2

Given that both rhombuses have sides of length 7, we can calculate the diagonals using the properties of rhombuses.

For the first rhombus with an angle of π/3, we can use trigonometric ratios to find the lengths of the diagonals. Since the angle given is π/3, which is 60 degrees in degrees, we can use the properties of a 30-60-90 triangle.

The ratio of the sides in a 30-60-90 triangle is 1:sqrt(3):2. Since the side length is 7, the shorter diagonal (which is opposite the 60-degree angle) would be 7 * sqrt(3) and the longer diagonal would be 7 * 2 = 14.

For the second rhombus with an angle of (5π)/8, we need to calculate the diagonals differently. We can use trigonometric ratios for this angle as well. However, since (5π)/8 is not a standard angle, we may need to use trigonometric identities to calculate the diagonals.

Once we have the lengths of the diagonals for both rhombuses, we can use the formula mentioned earlier to find their respective areas. After calculating the areas of both rhombuses, we can subtract the smaller area from the larger area to find the difference in their areas. This would give us the answer to the question.

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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 A, B, C, and D. Sides A and B have a length of #7 # and sides C and D have a length of # 6 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?
- A quadrilateral is a ______ if and only if its diagonals are perpendicular?
- A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?
- Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(11pi)/12 #, what is the difference between the areas of the rhombuses?

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