Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/4 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
Both rhombuses are identical and hence no difference in areas.
Given
Area of Rhombus
We know, sin theta = sin pi  theta)#
In both the rhombuses, theta is
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The area of a rhombus can be calculated using the formula ( A = \frac{1}{2} d_1 d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.
For a rhombus with side length ( s ) and a corner angle ( \theta ), the diagonals have lengths ( s ) and ( s\sqrt{2} ).
Using this information, we can calculate the areas of the two rhombuses:

For the rhombus with an angle of ( \frac{\pi}{4} ): [ A_1 = \frac{1}{2} \cdot 7 \cdot 7\sqrt{2} = 49\sqrt{2} ]

For the rhombus with an angle of ( \frac{3\pi}{4} ): [ A_2 = \frac{1}{2} \cdot 7 \cdot 7\sqrt{2} = 49\sqrt{2} ]
The difference between the areas is: [ \text{Difference} = A_1  A_2 = 49\sqrt{2}  49\sqrt{2} = 0 ]
So, the difference between the areas of the two rhombuses is 0.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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