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The cross-section of a canal is in the shape of a trapezium. If the canal is $12 c$ m wide at the bottom, $8 c$ m wide at the top and the area of its cross-section is 84 $c m^{2}$ , determine its depth.

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8.4

7.4

4.8

6.4

answer is A.

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Detailed Solution

Given that,
The cross-section of a canal is in the shape of a trapezium such that the canal is

12 c

m wide at the bottom,

8 c

m wide at the top and the area of its cross-section is 84

c m^{2}

.
Consider the figure of canal,
Question Image

We have to find the depth of the canal.
Area of a trapezium

= \frac{1}{2} \times

(sum of parallel sides)

\times

depth.

⇒ A = 12 × l 1 + l 2 × h

So, putting the respective values, we get,

84 = \frac{1}{2} \times (12 + 8) \times h

\Rightarrow 84 = \frac{20 h}{2}

\Rightarrow 84 = 10 h

\Rightarrow h = \frac{84}{10}

\Rightarrow h = 8.4 cm

Therefore, the depth of canal

= 8.4 cm

.
Hence, option 1 is correct.

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