the cross section of a canal is a trapezium in shape .if the canal is 10m wide at top ,6m wide at bottom & the area of the cross section is 72 sq m ,determine its depth
The area of a trapezium is
A = (Top+Bottom)*Height/2
Solve for Height:
H=2*Area/(Top+Bottom)
=2*72/(10+6)
=144/16
=?
144/16=
To determine the depth of the canal, we can use the formula for the area of a trapezium:
Area = (1/2) * (a + b) * h
Where:
- a and b are the lengths of the parallel sides (in this case, the widths of the top and bottom of the canal)
- h is the height or depth of the canal
Given:
- Width at the top (a) = 10m
- Width at the bottom (b) = 6m
- Area = 72 sq m
Let's substitute these values into the formula:
72 = (1/2) * (10 + 6) * h
Simplifying the expression:
72 = (1/2) * 16 * h
Dividing both sides of the equation by 8:
9 = h
Therefore, the depth of the canal is 9 meters.