If I am given the diagonals of a rhombus, how do I find the perimeter?


Quick Answer

Find the perimeter of a rhombus by taking half of each diagonal, summing their squares, square-rooting the result and finally multiplying by four. This method is derived from using the Pythagorean Theorem on one of the right triangles created by the diagonals in order to determine the length of one side. Since the sides of a rhombus are equal in length, multiplying that side by four equals the rhombus' perimeter.

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Full Answer

Since all four triangles created by the diagonals are congruent, any one of them can be used to find the perimeter. A rhombus is a geometric shape that is classified as a simple quadrilateral with all four sides having the same length. In terms of classification, every rhombus is a parallelogram, and a special rhombus where all the angles are equal to 90 degrees is classified as a square. Rhombi are also called diamonds when their four angles equal 60 degrees and are known as a lozenge when the angles are equal to 45 degrees. In a rhombus, the two diagonals are perpendicular to each other and bisect the opposite angles. It can be proven using congruent triangles that a rhombus is symmetric across its diagonals. This contrasts with a kite, where although the diagonals are perpendicular, only one of them is a line of symmetry.

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