Parallelogram – the geometrical figure which has lengths of the parallel parties and value of opposite corners are equal. The square, a rhombus and a rectangle also belong to this category.
Instruction
1. To find value of the area of a parallelogram it is necessary to know length of one of the parties and also height which is carried out to it. For descriptive reasons represent the schematic drawing, it will allow to choose an optimum method of the solution of a task.
2. The formula of finding of the area parallelograms looks as follows: S = a * Ha where an is the party; Ha is length of the diagonal which is carried out to the party of a. If height – the second necessary size is unknown, take one of the parties as a basis and carry out to it height which should be found. As the rectangular triangle was formed, it is possible to apply Pythagorean theorem: a = √c² – b², b = √c² – a²c = √a² + b²где an and b – the parties of a rectangular triangle; c – hypotenuse.
3. The course of search of lengths of the parties in many respects depends on basic data, in certain cases it is necessary to resort to trigonometry. a = with * cos β = with * sin α = b * tg αb = with * cos α = with * sin β = a * tg βc = a/sin α = a/cos β = b/cos α = b/sin βa and b – legs; c – hypotenuse. Calculation of length of height of a parallelogram with application of sine, cosines and tangents will require the reference book on the transfer of their values to number.
4. If before you a special case of a parallelogram, then for search of the area it is possible to use the simplified formulas. For example, to find this indicator in relation to a square it is important to know length of its party which should be multiplied on itself. S = a² where S is the area; a – party.
5. For search of value of the area of a rectangle substitute values of the parties in a formula: S = a * b; where an is length is one party; b – length to the party, perpendicular to a.
6. One more option of a parallelogram – a rhombus. To find value of its area, use one of formulas.S = a * b/2 where an and b – length of diagonals.S = a * Ha where Ha – length of the diagonal which is carried out to the party of a.S = by a² * sin α where α — a corner between two adjacent parties of a rhombus.