6. Other methods of constructing a rhombus

Let us look at the other two methods of constructing a rhombus.

Let us construct a rhombus with diagonals as \(8\) \(cm\) and \(9\) \(cm\) respectively. Let us also find the area of the rhombus thus formed.

 

Step \(1\): Draw a rough diagram with the known measurements.

 

 

Step \(2\): Draw a line segment \(DB\) of \(9\) \(cm\) length.

 

 

Step \(3\): Draw a perpendicular line to \(DB\) and mark the intersection as \(O\).

 

 

Step \(4\): With \(O\) as centre and with \(4\) \(cm\) as radius, draw two arcs on the perpendicular line and mark the intersections as \(A\) and \(C\) respectively.

 

 

Step \(5\): Join \(AD\), \(CD\), \(BC\) and \(AB\) to form the required quadrilateral.

 

 

To find the area of the rhombus:

 

\(\text{Area of the rhombus} = \frac{1}{2} \times d_1 \times d_2\)

 

 

\(= 36\) \(cm^2\)

Let us construct a rhombus with \(7\) \(cm\) as one of its diagonal and \(100^\circ\) as one of its angles.

 

Step \(1\): Draw a rough diagram with the known measurements.

 

 

Step \(2\): Draw a line segment \(DB\) of \(7\) \(cm\) in length.

 

 

Step \(3\): With \(D\) as centre, measure \(50^\circ\) draw a line on both the sides of the line segment.

 

 

Step \(4\): Similarly, with \(B\) as centre, measure \(50^\circ\) draw a line on both the sides of the line segment. Mark the intersections as \(A\) and \(C\) to get the desired rhombus.