In the following figure, $\mathrm{XY}$ is parallel to $\mathrm{BC}, \mathrm{AX} =9 \mathrm{cm}, \mathrm{XB} = 4.5 \mathrm{cm}$ and $\mathrm{BC} = 18 \mathrm{cm}.$

Find :
$\mathrm{XY}$

In the following figure, $\mathrm{ABCD}$ to a trapezium with $\mathrm{AB} // \mathrm{DC}.$ If $\mathrm{AB} = 9 \mathrm{cm}, \mathrm{DC} = 18 \mathrm{cm}, \mathrm{CF} = 13.5 \mathrm{cm}, \mathrm{AP} = 6 \mathrm{cm}$ and $\mathrm{EE} = 15 \mathrm{cm}.$ Calculate :

$\mathrm{EC}$

In the following figure, $\mathrm{ABCD}$ to a trapezium with $\mathrm{AB} // \mathrm{DC}.$ If $\mathrm{AB} = 9 \mathrm{cm}, \mathrm{DC} = 18 \mathrm{cm}, \mathrm{CF} = 13.5 \mathrm{cm}, \mathrm{AP} = 6 \mathrm{cm}$ and $\mathrm{EE} = 15 \mathrm{cm}.$ Calculate :

$\mathrm{AF}$

In the following figure, $\mathrm{ABCD}$ to a trapezium with $\mathrm{AB} // \mathrm{DC}.$ If $\mathrm{AB} = 9 \mathrm{cm}, \mathrm{DC} = 18 \mathrm{cm}, \mathrm{CF} = 13.5 \mathrm{cm}, \mathrm{AP} = 6 \mathrm{cm}$ and $\mathrm{EE} = 15 \mathrm{cm}.$ Calculate :

$\mathrm{PE}$

In the following figure, $\mathrm{AB}, \mathrm{CD}$ and $\mathrm{EF}$ are perpendicular to the straight line $\mathrm{BDF}.$

If $\mathrm{AB} = \mathrm{X}$ and, $\mathrm{CD} = \mathrm{z}$ unit and $\mathrm{EF} = \mathrm{y}$ unit, prove that :