# Two rhombuses have sides with lengths of #11 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

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The area of a rhombus is given by the formula ( A = \frac{1}{2} d_1 d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of its diagonals.

For the rhombus with an angle of ( \frac{\pi}{12} ), we can use trigonometry to find the lengths of its diagonals. Let ( d_1 ) be the longer diagonal and ( d_2 ) be the shorter diagonal.

( \sin\left(\frac{\pi}{12}\right) = \frac{d_2}{11} ) and ( \cos\left(\frac{\pi}{12}\right) = \frac{d_1}{11} ).

For the rhombus with an angle of ( \frac{7\pi}{8} ), similarly, let ( d_3 ) be the longer diagonal and ( d_4 ) be the shorter diagonal.

( \sin\left(\frac{7\pi}{8}\right) = \frac{d_4}{11} ) and ( \cos\left(\frac{7\pi}{8}\right) = \frac{d_3}{11} ).

Compute the lengths of the diagonals using these trigonometric relationships.

Then, use the area formula to find the areas of both rhombuses.

Finally, subtract the smaller area from the larger area to find the difference.

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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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- Two opposite sides of a parallelogram each have a length of #7 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #35 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(7pi)/12 #, what is the difference between the areas of the rhombuses?

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