8. Constructing a trapezium with four sides known

Construct a trapezium $ABCD$ in which $\overline{AB}$ is parallel to $\overline{CD}$, $AB$ $=$ $9$ $cm$, $BC$ $=$ $5$ $cm$, $CD$ $=$ $6$ $cm$ and $DA$ $=$ $6.5$ $cm$. Also, find its area.

 

Construction:

 

Step 1: Draw a line segment $AB$ $=$ $9$ $cm$.

 

Step 2: Mark a point $P$ on the line segment $AB$ such that $AP$ $=$ $6cm$.

 

Step 3: With $P$ and $B$ as centres, draw two arcs of radii $6.5$ $cm$ and $5$ $cm$ respectively such that they intersect each other at $C$.

 

Step 4: Join $PC$ and $BC$.

 

Step 5: With $C$ and $A$ as centres, draw two arcs of radii $6$ $cm$ and $6.5$ $cm$ respectively such that they intersect each other at $D$.

 

Step 6: Join $AD$ and $CD$.

 

Step 7: $ABCD$ is the required trapezium. The measure of $DQ$ gives the height of the trapezium $ABCD$.