The cross-section of a canal is in the shape of a trapezium. If the canal is 12 m wide at the top and 8 m wide at the bottom and the area of its cross-section is 84 m², determine its depth.

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Solution

Let the depth be h m Area of trapezium = 84 m²

rightwards double arrow

Area of

increment ABC

+ Area of

increment ADC

= 84 m²

rightwards double arrow space space 1 half left parenthesis AB right parenthesis left parenthesis DE right parenthesis plus 1 half left parenthesis DC right parenthesis left parenthesis DE right parenthesis equals 84 rightwards double arrow space space space 1 half left parenthesis 12 right parenthesis left parenthesis straight h right parenthesis plus 1 half left parenthesis 8 right parenthesis left parenthesis straight h right parenthesis equals 84 rightwards double arrow space space space space space space space 6 straight h plus 4 straight h equals 84 rightwards double arrow space space space space space space space space space space 10 straight h space equals space 84 rightwards double arrow space space space space space space space space straight h equals 84 over 10 equals 8.4

Hence, the depth of the canal is 8.4 m.

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