# Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(11pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

Difference in areas between the two rhombuses is 10.6408

Area of rhombus

Where

In this case we will use the formula Area = a * h.

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The area of a rhombus can be calculated using the formula:

[ \text{Area} = \frac{{d_1 \times d_2}}{2} ]

where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.

In this case, since the length of each side of the rhombuses is 4, the lengths of their diagonals can be found using trigonometry.

For each rhombus: [ d_1 = 4 \times \sin(\text{angle}) ] [ d_2 = 4 \times \sin(\frac{\pi}{2} - \text{angle}) ]

Calculate the diagonals for both rhombuses using the given angles, then find the areas using the formula mentioned above. Finally, find the difference between the areas of the two rhombuses.

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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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