Question:
The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 m2, find the depth of the canal.
Solution:
The top and the bottom of the canal are parallel to each other.
Let the height of the trapezium be h.
Area of trapezium $=\frac{1}{2} \times$ sum of parallel sides $\times$ height
$\Rightarrow 640=\frac{1}{2} \times(10+6) \times h$
$\Rightarrow 640=8 \times h$
$\Rightarrow h=\frac{640}{8}$
$\Rightarrow h=80 \mathrm{~m}$
Hence, the depth of the canal is 80 m.
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