# Two rhombuses have sides with lengths of #6 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

Difference in areas between the two rhombuses is 4.4592

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: Area = (diagonal1 * diagonal2) / 2.

The diagonals of a rhombus are perpendicular bisectors of each other, forming four right triangles within the rhombus.

Given that the sides of both rhombuses have lengths of 6, we can find the lengths of their diagonals using trigonometric functions.

For the rhombus with an angle of π/12: The angle π/12 is the acute angle formed by the diagonal and one side of the rhombus. Using trigonometric functions, we can find that the length of the diagonal is 6 * tan(π/12) = 6 * tan(15°).

For the rhombus with an angle of (7π)/8: The angle (7π)/8 is the acute angle formed by the diagonal and one side of the rhombus. Using trigonometric functions, we can find that the length of the diagonal is 6 * tan((7π)/8) = 6 * tan(157.5°).

Now, calculate the areas of both rhombuses using the formula mentioned earlier.

Then, find the difference between the areas of the two 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.

- What are real-life examples of parallelograms?
- Can a quadrilateral be both a rhombus and a rectangle? Please explain.
- A parallelogram has sides with lengths of #18 # and #4 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #36 #, how long are the other two sides?
- Do rhombuses, squares and rectangles all share properties of parallelograms?

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