How to find a diamond side

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How to find a diamond side?

The rhombus is an equilateral parallelogram.

Diamond properties:

  • the diagonal is a bisectrix;
  • The diagonals intersect at a point that divides them in half. The angle of intersection is 90 degrees;
  • opposite sides are parallel to each other;
  • if the rhombus has right angles, then this is a square.

The basic formulas are:

The area of ​​the rhombus S can be found by the following formulas:

  • S = ah
  • S = 2 · r · a, where r is the radius of the circle inscribed in the diamond, and a is the side of the diamond.
  • S = (d1 · d2) / 2, where d1 and d2 are the diagonals of the rhombus;

where:

  • a is the side of the diamond;
  • h - height;
  • d1 and d2 are diagonals;
  • r is the radius of the inscribed circle;

How to find a diamond side?

If we need to find a diamond side, then this can be done in several ways. Consider the example. The rhombus is ABCD. Its diagonals are AC and BD:

  1. Consider the unknown side as the hypotenuse of a right-angled triangle (half the diagonals of the rhombus - the legs of this triangle).rhombusWe recall the theorem of Pythagoras and find the right side. Namely, the sum of the squares of half the diagonals of the rhombus will be equal to the square of the desired side.
    • AB2= AO2+ BО2.
  2. If you know the area of ​​the diamond and one of its angles, then you can look for a side using the formula:
    • S = a2sinα
    • Where: a is the side of the rhombus;
    • α is the known angle between the sides.
    • From the previous formula, we deduce that the rhomb side can be calculated from the formula: a = √ (S / sinα)
  3. In the case where only diagonals are known, the side can be found by the formula:
    • a = (√D2+ d2) / 2
    • Where:
    • D - a large diagonal of the rhombus;
    • d is the smaller diagonal of the rhombus.

An example of solving a problem:

Find the side of the diamond. It is known that its diagonals are equal to 20 and 48 cm.

  • a = (√D2+ d2) / 2
  • a = (√482+202) / 2
  • a = (√2704) / 2
  • a = 26

Based on the properties of the diamond, we find that the sides are equal to each other and equal to 26 cm.



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