Question:
The cross-section of a canal is a trapezium in shape. If the canal is 10 m wide at the top 6 m wide at the bottom and the area of cross-section is 72 m2 determine its depth.
Solution:
Let the depth of canal be $d$.
Given:
Lengths of the parallel sides of the trapezium shape canal are $10 \mathrm{~m}$ and $6 \mathrm{~m}$.
And, the area of the cross section of the canal is $72 \mathrm{~m}^{2}$.
Area of trapezium $=\frac{1}{2} \times$ (Sum of the parallel sides) $\times$ (Perpendicular distance between the parallel sides)
$72=\frac{1}{2} \times(10+6) \times(d)$
$72=8 \times d$
$d=\frac{72}{8}=9 \mathrm{~m}$