The area of ​​the rhombus: formulas and facts

Rhombus (from the Greek and Latin ῥόμβος rombus «diamonds») is a parallelogram, which is characterized by the presence of equal length sides.In the case where the angles are 90 degrees (or at right angles) such geometric figure is called square.Diamond - a geometric shape, kind of quadrangles.It may be a square and a parallelogram.

The origin of the term

talk a little bit about the history of the figure that will reveal little for themselves puzzling mystery of the ancient world.Familiar to us the word frequently occurring in the school literature, "diamond" originates from the Greek word "drum".In ancient Greece, the musical instruments produced in the diamond-shaped or square (in contrast to the modern devices).Surely you have noticed that the card suits - diamonds - has a rhombic shape.The formation of this suit goes back to the days when the round diamonds are not used in everyday life.Therefore, the diamond - the most ancient historical figure, which was invented by mankind long before the wh


the first time such a word as "diamond" was used by well-known personalities such as Geron and Pope of Alexandria.

Properties rhombus

  1. Since the sides of the rhombus are opposite each other and are mutually parallel, the diamond is undoubtedly a parallelogram (AB || CD, AD || BC).
  2. Rhombus have a diagonal crossing at right angles (AC ⊥ BD), and, therefore, perpendicular.Hence, crossing divides in half diagonally.
  3. bisectors are the diagonal corners of the rhombic rhombus (∠DCA = ∠BCA, ∠ABD = ∠CBD and so on. D.).
  4. The identity of parallelograms that the sum of the squares of the diagonals of a rhombus square of the number of parties is multiplied by 4.

Signs rhombus

in cases Rhombus is a parallelogram that meets the following conditions:

  1. Allsides of the parallelogram are equal.
  2. diagonals of a rhombus intersect at right angles, so they are perpendicular to each other (AC⊥BD).This proves that the rule of three sides (the sides are equal and are at an angle of 90 degrees).
  3. diagonals of a parallelogram divide corners equally, as the sides are equal.

Area rhombus

Area rhombus can be calculated by means of several formulas (depending on the material provided in the problem).Then read about what is the area of ​​rhombus.

  1. rhombus area equal to the number that is half the product of its diagonals.
  2. Since diamond - a kind of a parallelogram, the area of ​​the rhombus (S) is the number of the product side of the parallelogram on the height (h).
  3. Furthermore, the area of ​​the rhombus may be calculated by a formula which is the product of the squared sides by the sine of the angle of the rhombus.The sine of the angle - alpha - the angle located between the sides of the original diamond.
  4. quite acceptable for the right decision is considered to be a formula which is the product of twice the angle alpha and the radius of the inscribed circle (r).

These formulas you can calculate and prove on the basis of the Pythagorean theorem and the rules of the three sides.Many examples focus on the involvement of several formulas in a single job.