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properties of a rhombus properties of a rhombus a rhombus is four sided figure that is a special type of quadrilateral it is sometimes represented by symbol a rhombus is a convex parallelogram in which every one of the four sides are equivalent in magnitude it is a diamond shape figure as shown in the figure below the properties of a rhombus make it special if compared to a simple parallelogram we have described these properties of a rhombus using a particular abcd in the following subdivision 1 a rhombus is sometimes called an equilateral quadrilateral as all its four sides are equal in other words we can write ab bc cd da 2 every rhombus can be considered to b a parallelogram but vice versa is not true thus all properties that hold true for a general parallelogram are also true for a rhombus thus opposite sides are parallel and equal opposite angles are also identical in degrees know more about area moment of inertia math.tutorvista.com page no 1/4

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p. 2

3 a rhombus is similar to a square if we take into account the facts that all sides are equal and opposite sides are parallel however the difference is that all angles of a square are equal and their measurement is 90o thus a square is a special case of a rhombus in addition out of all possible rhombuses of equivalent sides a square has maximum area 4 the diagonals i.e lines ac and db bisect the angles they contain i.e ac cuts in half angles a and c and diagonal bd bisects angles b and d additionally they also divide each other in exact halves at the point of intersection of diagonals four 90o angles are formed as a result we can conclude that diagonals in a rhombus bisect each other at 90o a point to be noted is that the diagonals may or may not be equal if the diagonals are equal in a rhombus then it is essentially a square 5 to find perimeter of a rhombus simply sum up the magnitudes of all four sides or multiply the magnitude of a side with 4 we can write perimeter of a rhombus ab bc cd da if ab bc cd da x then perimeter of a rhombus 4 x 6 there are various ways to find the area of a rhombus if its height and length of a base are known then area is calculated as follows area of a rhombus base height 2 i.e if base x and height y then learn more polar moment of inertia math.tutorvista.com page no 2/4

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area of a rhombus x y 2 if the lengths of the diagonals are known then area is calculated as follows area of a rhombus diagonal1 diagonal2 2 where diagonal1 and diagonal2 are lengths of two diagonals ac and bd 7 the sum of the adjacent angles in a rhombus is equal to 180o a b 180o c d 180o 8 in a rhombus the total sum of the squares of the sides consider length of each side to be x units is the same as the total sum of the squares of the diagonals consider the length of diagonal1 to be d1 units and the length of diagonal2 to be d2 units mathematically it can be written as d12 d22 4 x2 math.tutorvista.com page no 4/4

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p. 4

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