### 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**:

**: Draw a line segment \(JU\) \(=\) \(8.5\) \(cm\).**

*Step 1***: With \(U\) as centre, mark an angle \(75^{\circ}\) using a protractor and mark it as \(X\). Join \(QX\).**

*Step 2***: With \(J\) as centre, draw an arc of radius \(9\) \(cm\) intersecting \(QX\) at \(M\). Join \(JU\).**

*Step 3***: Measure \(UM\), and with \(J\) as centre, draw an arc of radius that is equal to the measure of \(UM\).**

*Step 4***: With \(M\) as centre, draw an arc of radius \(8.5\) \(cm\) intersecting the previous arc at \(P\).**

*Step 5***: Join \(MP\) and \(MJ\).**

*Step 6***: \(JUMP\) is the required parallelogram. The measure of \(MA\) gives the height of the parallelogram \(JUMP\).**

*Step 7*Area calculation:

Area of the parallelogram \(=\) \(base \times height\) square units

\(=\) \(8.5 \times 5.6\)

\(=\) \(47.60\) \(cm^2\)