Question

cross section of a canal is in the shape of a trapezium .if canal is 12m wide at the top and 8m wide at the bottom and area is 84msq.,determine depth:

Answer 1

We know,

Area of trapezium = $\frac{1}{2}\times \mathrm{sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\times \mathrm{height}=\frac{1}{2}\times (a+b)\times h$

Now, a = 12 m, b = 8 m and height = h and area of trapezium = 84 m²

So, putting the respective values, we get

Area of trapezium $=\frac{1}{2}\times (a+b)\times h$

$$\begin{gathered} \Rightarrow 84=\frac{1}{2}\times \left(12+8\right)\times h \\ \Rightarrow 84\times 2=20\times h \\ \Rightarrow \frac{84\times 2}{20}=h \\ \Rightarrow h=\frac{84}{10}=8.4m \end{gathered}$$

Thus, height = 8.4 m