7. Constructing a trapezium with two sides and two angles

Construct a trapezium $PQRS$ in which $\overline{PQ}$ is parallel to $\overline{RS}$, $PQ$ $=$ $8.5$ $cm$, $QR$ $=$ $6.5$ $cm$, $\angle PQR$ $=$ $75^{\circ}$ and $\angle QPS$ $=$ $110^{\circ}$. Also, find its area.

 

Construction:

 

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

 

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

 

Step 3: With $Q$ as centre, draw an arc of radius $6.5$ $cm$ intersecting $QX$ at $R$.

 

Step 4: Draw a line $RY$ parallel to $PQ$.

 

Step 5: With $P$ as centre, mark an angle $110^{\circ}$ using a protractor and mark it as $Z$. Join $PZ$ intersecting $QY$ at $S$.

 

Step 6: $PQRS$ is the required trapezium. The measure of $RA$ gives the height of the trapezium.