The cross-section of a canal is a trapezium in shape.

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)

$72=\frac{1}{2} \times(10+6) \times(d)$

$72=8 \times d$

$d=\frac{72}{8}=9 \mathrm{~m}$

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