How to find the area of a rhombus

How to find the area of a rhombus

The rhombus is introduced for the first time by Ancient Greek mathematicians Heron and Pappa Aleksandriysky. The rhombus has 4 corners and 4 parties, but not at once itself can imagine its look. In translation from Greek (qouboc - "tambourine") - it is a usual quadrangle at which the opposite parties are equal and in pairs parallel. And it is possible to call a rhombus with right angles a square safely.


1. To determine the area, it is necessary to study even small list of the properties belonging to a rhombus: - opposite corners are always equal; - diagonals are perpendicular to each other; - also diagonals in a point of intersection are halved; - diagonals halve corners therefore are also bisectors; - the corners adjacent to one party, in the sum give 180 °; It was in detail written about rhombus diagonals that not for nothing because they are used in a formula for finding of the area. The first formula: S=d1*d2/2 where d1, d2 - are rhombus diagonals.

2. The second formula uses the rhombus corner adjacent to one of the parties which are also used in calculation.S=a*2sin (α) where an is the party of a rhombus; α - a corner between the parties of a rhombus. To find from this corner the sine will not make complexity if at you the calculator is had near at hand or you will find values in the special table of sine.

3. The formula calculation of the area of a rhombus containing a sine of the angle not only. There is a following method: S=4r^2/sin(α). All values are known and clear, except the appeared r is the maximum radius of a circle which can be located in a figure.

4. And last formula: S=a*H where an as it was specified in advance, is the party; N - rhombus height.

Author: «MirrorInfo» Dream Team