# 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)/4 #, what is the difference between the areas of the rhombuses?

Difference in areas between the two rhombuses is 7.1724

Area of rhombus

Where

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

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To find the difference between the areas of the rhombuses, we first need to calculate the areas of both rhombuses.

The area ( A ) of a rhombus can be calculated using the formula ( A = \frac{1}{2} \times d_1 \times d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.

For a rhombus with side length ( s ) and an angle ( \theta ) at one of its corners, the diagonals are given by ( d_1 = s ) and ( d_2 = s \cdot \sqrt{2 - 2\cos(\theta)} ).

Given that both rhombuses have side lengths of 4, and using the angles provided:

For the first rhombus with angle ( \frac{11\pi}{12} ): [ d_1 = 4 ] [ d_2 = 4 \cdot \sqrt{2 - 2\cos\left(\frac{11\pi}{12}\right)} ]

For the second rhombus with angle ( \frac{3\pi}{4} ): [ d_1 = 4 ] [ d_2 = 4 \cdot \sqrt{2 - 2\cos\left(\frac{3\pi}{4}\right)} ]

Now, calculate the areas of both rhombuses using the formula ( A = \frac{1}{2} \times d_1 \times d_2 ) for each.

Finally, subtract the smaller area from the larger area to find the difference between the areas of the 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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- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #(pi)/2 # 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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