If all parties of a flat geometrical figure with the parallel opposite sides (parallelogram) are equal, diagonals are crossed at an angle in 90 ° and halve corners in polygon tops, then it is possible to call it a rhombus. These additional properties of a quadrangle considerably simplify formulas finding of its area.
Instruction
1. If lengths of both diagonals of a rhombus are known (E and F), for finding of the area of a figure (S) calculate value of a half of the work of these two sizes: S=½*E*F.
2. If in statements of the problem length of one of the parties (A) and also height (h) of this geometrical figure is given, then for finding of the area (S) use the formula applied to all parallelepipeds. Height is the piece perpendicular to the party connecting it to one of rhombus tops. The formula of calculation of the area with use of these data is very simple - they should be multiplied: S=A*h.
3. If basic data contain data on the size of an acute angle of a rhombus (α) and length of its party (A), then for calculation of the area (S) it is possible to use one of trigonometrical functions - a sine. Multiply the squared length of the party by a sine of the known corner: S=A²*sin(α).
4. If the circle of the known radius (r) is entered in a rhombus, and length of the party (A) is given in statements of the problem too, then for finding of the area (S) of a figure multiply these two sizes, and double the received result: S=2*A*r.
5. If except the radius of an inscribed circle (r) only the size of an acute angle (α) of a rhombus is known, then in this case too it is possible to use trigonometrical function. Divide the squared radius into a sine of the known corner, and increase the received result four times: S=4*r²/sin(α).
6. If this geometrical figure is known that it is a square, that is a special case of a rhombus with right angles, then for calculation of the area (S) the nobility only length of the party (A) is enough. Just square this size: S=A².
7. If it is known that about a rhombus it is possible to describe a circle of the set radius (R), then this value is enough for calculation (S) Square. It is possible to describe a circle only about a rhombus which sizes of corners are identical, and the radius of a circle will coincide with half of lengths of both diagonals. Substitute the corresponding values in a formula from the first step and find out that the area in this case can be found, doubling the squared radius: S=2*R².