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

Answer 1

#11.314-4.141 =7.173#

Area of rhombus #= bxxh#

Rhombus 1 :

#h=4sin15= 1.0353#

Area 1 (A1) #= 4xx1.0353 = 4.141#

Rhombus 2:

#h=4sin45=2.8284#

Area 2 (A2) #=4xx2.8284=11.314#

Difference between A1 and A2 :

#=> 11.314-4.141 = 7.173#

Or solution 2 :

difference of areas :

#4(4sin45-4sin15)=7.173#

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Answer 2

To find the difference between the areas of the two rhombuses, first, determine the diagonals of each rhombus.

For the rhombus with an angle of ( \frac{11\pi}{12} ), the diagonals are 4 and (4 \tan\left(\frac{11\pi}{24}\right)).

For the rhombus with an angle of ( \frac{\pi}{4} ), the diagonals are both 4.

Calculate the area of each rhombus using the formula: Area = ( \frac{d_1 \times d_2}{2} ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.

Finally, find the difference between the areas of the two rhombuses.

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Answer from HIX Tutor

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.

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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