# What is the area of a rhombus?

Half the product of the length of the two diagonals.

The area of a rhombus is half of the enclosing rectangle.

The area of the rectangle is the product of the lengths of the two diagonals of the rhombus.

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Divide the rhombus into two triangles, then solve for area.

In the image below, we can break the rhombus ABCD into two triangles, BAD and BCD. Then, we can solve the area of one of the triangles, then multiply by 2 to account for both.

Triangle BCD has a height of 20, but we do not know the base. However, we can break BCD into two right triangles. Then we use the Pythagorean Theorum to figure out that line BO is about 22. 22*2 gives us the base of the triangle, because there are two right triangles with the base of 22.

Now we can calculate for the area of one of the triangles.

Then, we have to multiply by two to give us the area of the rhombus, because there are two triangles.

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The area of a rhombus can be calculated using the formula:

[ \text{Area} = \frac{d_1 \times d_2}{2} ]

Where (d_1) and (d_2) are the lengths of the diagonals of the rhombus. Alternatively, the area can also be calculated using the formula:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]

Where the base and height are the lengths of any two perpendicular sides of the rhombus.

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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 is a quadrilateral with no right angles?
- Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/8 #, what is the difference between the areas of the rhombuses?
- Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/3 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 1 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?
- A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #45 #, what is the length of its longest diagonal?

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