Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?
Now, the difference of areas of rhombus
By signing up, you agree to our Terms of Service and Privacy Policy
The difference between the areas of the two rhombuses is 18 square unitsThe difference between the areas of the two rhombuses can be found by using theThe difference between the areas of the two rhombuses is 18 square units.The difference between the areas of the two rhombuses can be found by using the formula for the area of a rhombus, which is ( 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, the diagonals are perpendicular bisectors of each other, meaning that they intersect at right angles.
To find the lengths of the diagonals, we use trigonometry:

For the rhombus with an angle of ( \frac{7\pi}{12} ):
 The diagonals bisect the angle, so each diagonal forms an angle of ( \frac{7\pi}{24} ) with one side of the rhombus.
 Using trigonometric ratios, we can find the lengths of the diagonals.
 Let ( x ) be half the length of one diagonal. Then ( \tan\left(\frac{7\pi}{24}\right) = \frac{9}{x} ).
 Solving for ( x ), we get ( x = \frac{9}{\tan\left(\frac{7\pi}{24}\right)} ).
 Since the diagonals are perpendicular, their lengths are equal, so the length of each diagonal is ( 2x ).

For the rhombus with an angle of ( \frac{\pi}{4} ):
 Similar to the previous rhombus, the diagonals bisect the angle, forming angles of ( \frac{\pi}{8} ) with one side of the rhombus.
 Let ( y ) be half the length of one diagonal. Then ( \tan\left(\frac{\pi}{8}\right) = \frac{9}{y} ).
 Solving for ( y ), we get ( y = \frac{9}{\tan\left(\frac{\pi}{8}\right)} ).
 Again, since the diagonals are perpendicular, their lengths are equal, so the length of each diagonal is ( 2y ).
Now, we can find the areas of the two rhombuses using the formula mentioned earlier, and then calculate the difference between their areas.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
 Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #54 #, how long are the other two sides?
 Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/8 # and the other has a corner with an angle of #(5pi)/12 #, what is the difference between the areas of the rhombuses?
 A parallelogram has sides with lengths of #16 # and #8 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?
 A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?
 A parallelogram has sides A, B, C, and D. Sides A and B have a length of #9 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(5 pi)/12 #, what is the area of the parallelogram?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7