Theory:

Let us look at the other two methods of constructing a rhombus.
Method \(3\): When two diagonals are given
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.
 
1324_20.svg
 
Step \(2\): Draw a line segment \(DB\) of \(9\) \(cm\) length.
 
1324_21.svg
 
Step \(3\): Draw a perpendicular line to \(DB\) and mark the intersection as \(O\).
 
1324_22.svg
 
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.
 
1324_23.svg
 
Step \(5\): Join \(AD\), \(CD\), \(BC\) and \(AB\) to form the required quadrilateral.
 
1324_24.svg
 
To find the area of the rhombus:
 
\(\text{Area of the rhombus} = \frac{1}{2} \times d_1 \times d_2\)
 
\(= \frac{1}{2} \times 9 \times 8\)
 
\(= 36\) \(cm^2\)
Method \(4\): When one diagonal and one angle is given
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.
 
1324_25.svg
 
Step \(2\): Draw a line segment \(DB\) of \(7\) \(cm\) in length.
 
1324_26.svg
 
Step \(3\): With \(D\) as centre, measure \(50^\circ\) draw a line on both the sides of the line segment.
 
1324_27.svg
 
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.
 
1324_28.svg
 
To find the area of the rhombus:
 
\(\text{Area of the rhombus} = \frac{1}{2} \times d_1 \times d_2\)
 
We know that \(DB = 7\) \(cm\). Let \(DB\) be \(d_1\).
 
To know the length of \(AC\), we should measure the length manually.
 
When measured, \(AC = d_2 = 5.9\) \(cm\).
 
\(= \frac{1}{2} \times 7 \times 5.9\)
 
\(= 20.65\) \(cm^2\)