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

Method \(3\): When two diagonals are given

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**:

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

\(= \frac{1}{2} \times 9 \times 8\)

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

Method \(4\): When one diagonal and one angle is given

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.

**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, \(AC = d_2 = 5.9\) \(cm\).

\(= \frac{1}{2} \times 7 \times 5.9\)

\(= 20.65\) \(cm^2\)