### Theory:

Working rule to construct a parallelogram:

Let us discuss the working rule to construct a parallelogram when the measure of one side, one angle and one diagonal of a parallelogram are given.
Example:
Construct a parallelogram $$JUMP$$ with $$JU$$ $$=$$ $$8.5$$ $$cm$$, $$JM$$ $$=$$ $$9$$ $$cm$$ and $$\angle JUM$$ $$=$$ $$75^{\circ}$$. Also, find its area.

Construction:

Step 1: Draw a line segment $$JU$$ $$=$$ $$8.5$$ $$cm$$.

Step 2: With $$U$$ as centre, mark an angle $$75^{\circ}$$ using a protractor and mark it as $$X$$. Join $$QX$$.

Step 3: With $$J$$ as centre, draw an arc of radius $$9$$ $$cm$$ intersecting $$QX$$ at $$M$$. Join $$JU$$.

Step 4: Measure $$UM$$, and with $$J$$ as centre, draw an arc of radius that is equal to the measure of $$UM$$.

Step 5: With $$M$$ as centre, draw an arc of radius $$8.5$$ $$cm$$ intersecting the previous arc at $$P$$.

Step 6: Join $$MP$$ and $$MJ$$.

Step 7: $$JUMP$$ is the required parallelogram. The measure of $$MA$$ gives the height of the parallelogram $$JUMP$$. Area calculation:

Area of the parallelogram $$=$$ $$base \times height$$ square units

$$=$$ $$8.5 \times 5.6$$

$$=$$ $$47.60$$ $$cm^2$$