# Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?

Difference in areas between the two rhombuses is 54.2655

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{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2 ).

For a rhombus with side length ( s ) and an angle ( \theta ) between two adjacent sides, the diagonals are ( d_1 = s ) and ( d_2 = s \times \text{abs}(2\sin(\theta)) ).

Given:

- Both rhombuses have side lengths of 15.
- One rhombus has a corner angle of ( \frac{\pi}{12} ) radians.
- The other rhombus has a corner angle of ( \frac{5\pi}{6} ) radians.

Let's calculate the areas of both rhombuses using the formula mentioned above.

For the rhombus with angle ( \frac{\pi}{12} ):

- ( d_1 = 15 )
- ( d_2 = 15 \times \text{abs}(2\sin(\frac{\pi}{12})) )

For the rhombus with angle ( \frac{5\pi}{6} ):

- ( d_1 = 15 )
- ( d_2 = 15 \times \text{abs}(2\sin(\frac{5\pi}{6})) )

Calculate the areas of both rhombuses using these diagonal lengths and then find the difference.

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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.

- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #7 # and sides C and D have a length of # 6 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram have lengths of #15 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #45 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #18 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #54 #, how long are the other two sides?
- In an isosceles trapezoid ABCD, AB=CD=5. The top base = 8 and the bottom base = 14. What is the area of this trapezoid?
- A parallelogram has sides with lengths of #12 # and #6 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

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