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### Theory:

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*Working rule to construct a trapezium*Let us discuss the working rule to construct a trapezium when the measure of three sides and one angle of a trapezium are given.

Example:

Construct a trapezium \(FINE\) in which \(\overline{FI}\) is parallel to \(\overline{NE}\), \(FI\) \(=\) \(8.5\) \(cm\), \(IN\) \(=\) \(6.5\) \(cm\), \(FE\) \(=\) \(7.5\) \(cm\) and \(\angle FIN\) \(=\) \(75^{\circ}\) at \(I\).

Construction:

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

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

**Step 2***: With \(I\) as centre, draw an arc of radius \(6.5\) \(cm\) intersecting \(IX\) at \(N\).*

**Step 3***: Draw a line \(NY\) parallel to \(FI\).*

**Step 4***: With \(F\) as centre, draw an arc of radius \(7.5\) \(cm\) intersecting \(NY\) at \(E\).*

**Step 5***: Join \(FE\). The measure of \(NA\) gives the height of the required trapezium \(FINE\).*

**Step 6**