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How to find the area of ​​a rhombus

How to find the area of ​​a rhombus

Diamond for the first time introduced the ancient Greek mathematician Heron of Alexandria and Pappa.

Diamond has 4 corners and 4 sides, but not immediately possibleimagine his appearance. Translated from the Greek (qouboc - tambourine?) - It is a regular quadrilateral whose opposite sides are equal and mutually parallel.

A diamond with right angles can be called a square.

instructions

1

To determine the area, you need to familiarize yourself with another short list of properties owned by a diamond:
- Opposite corners always ravny-

- Diagonal perpendicular to each drugu-

- Also diagonal at the intersection divided popolam-

- Diagonally divided in two corners, and are therefore bissektrisami-

- Corners adjacent to one side in total to 180 ° -

More has been written about the diagonals of a rhombus, which is not in vain, because they are used in the formula for finding the area.
The first formula: S = d1 * d2 / 2, where d1, d2 - are the diagonals of a rhombus.

2

The second formula uses the rhombus angle adjacent to one of the parties, which is also used in the calculation.

S = a * 2sin, where a (?) - Romba- side? - The angle between the sides of the diamond. Find the sine of the given angle will not be difficulty if you have a calculator handy, or you will find value in the special table of sines.

3

The formula of calculating the area of ​​a rhombus containing the sine of the angle, not the only one. There are the following method:
S = 4r ^ 2 / sin (?). All values ​​are known and understood, in addition to the pop-r - is the maximum radius of a circle that can fit in the figure.

4

The final formula is:

S = a * H, where a, As specified in advance - by the Parties is H - the height of the diamond.

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