The cross-section area of the embankment of a canal considered in calculation of earthwork for 'fully in embankment' case is given by:

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  1. [(b1 + b2) h + sh2]/2
  2. (b1 + b2) h + sh2
  3. (b1 + b2) h + 2sh2
  4. (b1 + b2) h + [sh2/2]

Answer (Detailed Solution Below)

Option 3 : (b1 + b2) h + 2sh2
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Detailed Solution

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Explanation:

Given,

b1 = Formation width

h = Height of the embankment

S:1 = Side slope of the embankment (H: V)

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The area of embankment = The area of the trapezium

Area of Trapezium = \(\frac{1}{2}\) × (Sum of Lengths of parallel sides) × Height

Area of Embankment 1 \(= \frac{1}{2}\left[ {b_1 + \left( {b_1 + 2sh} \right)} \right] \times h\)

A1 = b1h + sh2

Similarly the area of embankment 2 = A2 = \(= \frac{1}{2}\left[ {b_2 + \left( {b_2 + 2sh} \right)} \right] \times h\) =  b2h + sh2

Total area = A1 + A2 =  b1h + sh2 + b2h + sh2 = (b1 + b2) h + 2sh2

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