# Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/6 #, what is the difference between the areas of the rhombuses?

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To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2. For a rhombus with side length ( s ) and acute angle ( \theta ), the diagonals have lengths ( d_1 = s/\sin(\theta) ) and ( d_2 = s/\sin(\pi/2 - \theta) ).

Using this information, the area of the rhombus with angle ( \frac{7\pi}{12} ) is ( A_1 = \frac{(3/\sin(7\pi/12))^2}{2} ). The area of the rhombus with angle ( \frac{\pi}{6} ) is ( A_2 = \frac{(3/\sin(\pi/6))^2}{2} ).

Calculate both areas and find the difference: ( A_1 - A_2 ).

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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 #4 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/8 #, what is the area of the parallelogram?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #8 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?
- The exterior angles of a quadrilateral have measures of 72∘, 58∘, 2x∘, and 3x∘. How do I find the value of x?
- Two opposite sides of a parallelogram have lengths of #3 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #32 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #(pi)/6 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?

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