Rhombus — a special case of a parallelogram which all four parties are equal. On the plane it is better to apply the term "party", but not "edge" at designation of pieces of the straight lines limiting the area of a figure.
Instruction
1. To find the party of a rhombus of b — it means to express it through other parameters of a figure. If the perimeter P rhombuses is known, then it is enough to divide this size into four, and the party of a rhombus is found: b=P/4.
2. At the known area S rhombuses for calculation of the party of b it is necessary to know one more parameter of a figure. H height lowered from rhombus top on its party, or a corner β between the parties of a rhombus, or radius of r circle entered in a rhombus can be such size. The area of a rhombus, as well as the area of a parallelogram, is equal to the work of the party on height lowered on this party. From a formula S=b*h the party of a rhombus is calculated so: b=S/h.
3. If the area of a rhombus and one of its corners, these data is known too there is enough for finding of the party of a rhombus. When determining the area through an internal corner: S=b²*Sin β the party of a rhombus is determined by a formula: b= √ (S/Sinβ).
4. If the circle of the known radius of r is entered in a rhombus, then the area of a figure can be determined by a formula: S=2b*r as it is obvious that the radius of the circle entered in a rhombus is equal to a half of its height. At known the area and radius of an inscribed circle find the party of a rhombus on a formula: b=S/2r.
5. Diagonals of a rhombus are mutually perpendicular and divide a rhombus into four equal rectangular triangles. In each of these triangles a hypotenuse — the party of b of a rhombus, one leg a half of smaller diagonal of a rhombus of d /2, the second leg — a half of bigger diagonal of a rhombus of d /2. If d rhombus diagonals ₁ and d ₂ are known, then the party of a rhombus of b is determined by a formula: b² = (d /2)² + (d /2)²= (d ₁² + d ₂²)/4. It was necessary to take a square root from the received result, and the party of a rhombus is defined.