Rhombus - a geometric shape, in which all four sides are smooth. Not to be confused with rhombus parallelogram, whose parallel sides are equal. Another characteristic feature of the rhombus is that opposite corners therein are also equal, and in the diagonal intersection point form a right angle.
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How to find the perimeter of a rhombus? It is enough to know only one value - the length of the side. Since the perimeter is the length of the closed loop, the value for our figure will be equal to the product side by 4, because the figure four equal sides.
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The geometry does not always solve problems so simple. Quite often, the terms of the job side of unknown length. How to find the perimeter of the figure, if not of this magnitude? Given a diagonal, the perimeter can be found using the Pythagorean theorem. Let one diagonal is 8 cm, and the other 4 cm. In this case, half of them are 4 and 2 cm, respectively. This is the legs of a right triangle and its hypotenuse - side of the rhombus, which we need to calculate.
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By the theorem of Pythagoras the hypotenuse - is the square root of the sum of the squares of the legs, that is, side l 2=42+22\u003d 20. Remove the square root of the result, and will get the side of a rhombus or hypotenuse of a right triangle formed by the diagonals of a rhombus. In our case rhombus side 4.5 cm, respectively, the perimeter will be 4.5 * 4 \u003d 18 cm.
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The problems are sometimes known values \u200b\u200bare two diagonals on geometry, but only one. In that case, even given one of the corners of the diamond. If the angle of the rhombus is equal to 60 degrees, and the length of a diagonal equal to 10 cm, it is possible to calculate the length of a side of the rhombus by the formula, using Pythagoras theorem. Accordingly, the angle of direct triangle formed by diagonals is equal to 60/2 \u003d 30 degrees. Then the length of the leg is 10/2 \u003d 5 cm in order to find the length of the hypotenuse, use the formula.:
Lgipotenuzy \u003d Lkateta * cos (α)
In our case, the hypotenuse length is 5 * COS30 \u003d 5 * 0.87 \u003d 4.35 cm. Then the perimeter of the desired figure is 4.35 * 4 \u003d 17.4 cm. Use the engineering calculator for calculations or a special table from the school year of geometry, where sinuses and cosine of the main corners are indicated.
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You can calculate the perimeter, knowing the area of \u200b\u200bthe shape and its diagonal. In this case, we can calculate the length of the second diagonal and find the side of the rhombus on the Pythagora theorem. The area of \u200b\u200bthe figure is s \u003d (d1 + d2) / 2. Then D2 \u003d 2S / D1. If the area of \u200b\u200bthe desired figure is 18 cm, and one of the diagonals of 8 cm, then the length of the second diagonal is 2 * 18/8 \u003d 4.5 cm. According to the Pythagora theorem we find the hypotenuse, the square of which is equal to the sum of the squares of half the diagonals. We get that the square of hypotenuse 4 2+2,252\u003d 16 + 5 \u003d 21. Remove the square root and get 4.6 cm. Then the perimeter of the figure can be calculated by the formula 4.6 * 4 \u003d 18.4 cm.
As you can see, it is easy to calculate the perimeter of rhombus, it is necessary to know the simplest theorems and axioms of geometry. The basis of the Pythagora theorem, as well as the formula for determining the length of hypotenuses in the corners of the rectangular triangle. If it is difficult to figure out the corners, draw a triangle and mark its corners.
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