### 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.

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
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.

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, $$AC = d_2 = 5.9$$ $$cm$$.

$$= \frac{1}{2} \times 7 \times 5.9$$

$$= 20.65$$ $$cm^2$$