6. Constructing a trapezium with three sides and an angle

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:

 

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

 

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

 

Step 3: With $I$ as centre, draw an arc of radius $6.5$ $cm$ intersecting $IX$ at $N$.

 

Step 4: Draw a line $NY$ parallel to $FI$.

 

Step 5: With $F$ as centre, draw an arc of radius $7.5$ $cm$ intersecting $NY$ at $E$.

 

Step 6: Join $FE$. The measure of $NA$ gives the height of the required trapezium $FINE$.