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» Home » Geometry »

Area of Rhombus

          A rhombus is a quadrilateral having all sides with unequal diagonals, which bisect each other.
Note: If a square is pressed from two opposite corners, the rhombus is formed.

Let  be a rhombus then its area can be evaluated in two ways:


(1) When one side and the include angle is given:
            Let one side be equal to “” with include angle. Since, the diagonal divides the rhombus into two equal triangle, therefore


            Area of the rhombus
                                             
                                             
            Area of the rhombus

(2) When two diagonal are given:
            Let  and  be the length of the diagonal  and  respectively and since, the rhombus is divided into four equal triangles, therefore


            Area of the rhombus
                                             
                                             
                                             
            Area of the rhombus


Example:
            The length of each side of a rhombus is cm and two of its opposite angles are  each. Find the area.
Solution:
            Given that each side,  and
            Area of the rhombus
                                              
                                             
                                               square cm

Example:
            The diagonal of a rhombus are m and m. Find its area.
Solution:
            Given that diagonal are m and m


            Area of the rhombus
                                             
                                               Square m




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