As per below method how to find Trapezoidal footing volume (Isolated Footing Formula)
In this method drive formula of trapezoidal footing as per drawing specification
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Trapezoidal Footing Formula (Trapezoidal Footing Volume Formula)
As shown in Fig of trapezoidal footing. In this footing, two different parts show in fig.


 Rectangle/ Square Cubic Area
 Truncated Pyramid Area

Trapezoidal Footing =
Rectangle/ Squared Cubic Area (V1)
Truncated Pyramid Area (V2)
The volume of trapezoidal footing (Footing Calculation)
= Rectangle/ Square cubic area (V1) + Truncated Pyramid Area (V2)
V = V1 +V2
V = Volume of Trapzodial Footing.(Area of Trapezoidal Footing / Trapezoidal VolumeFormula)
V1 = Rectangle/ Square Cubic Area (V1)
Rectangle Cubic Area
 V1 = L x B x H
 L = Length of the cuboid = m. / mm.
 B = Breadth of the cuboid = m. / mm.
 H = Hight of the cuboid = m. / mm.
V2 = Truncated Pyramid Area (V2)
Truncated Pyramid Area (V2)
 V2 = (h/3) (A1 + A2 +√(A1 . A2))
 A1 = L1 x B1 = Sq.m /Sq. mm
 A1 = Truncated Pyramid Bottom Area
 A1 = L2 x B2 = Sq.m /Sq. mm
 A2 = Truncated Pyramid Top Area
 h = Height of Truncated Pyramid = M. / MM.
Derive Trapezoidal Pyramid Formula.(Trapezoidal Formula)
 V2 = (h/3) (A1 + A2 +√(A1 + A2))
One Cubicl = Six part of Truncated Pyramid
 V2 =Truncated Pyramid Area
 Cubic = 1/6 Truncated Pyramid area
 A^{3} =1/6 Truncated Pyramid Area
Truncated PyramidArea
= 1/6 A^{3}
= 1/6 (ab) ^{3}
= 1/6 (ab) (a^{2} + b^{2} +ab )
ab = 2h
a^{2} = a x a = A1
b^{2} = b x b = A2
= 1/6 . 2h. (a^{2} + b^{2} +ab )
=1/3. h. (a^{2} + b^{2} +ab )
=1/3 . h. (a + b + √(a.b))
=1/3. h. (A1 + A2 +√(A1.A2))
Example : Calculation Using Trapezoidal Footing Formula
The trapezoidal footing formula could be explained with an example. Consider a trapezoidal footing arrangement as shown in as per below fig.
Elevation of Trapezoidal Footing
Plan of Trapezoidal Footing
Here, a square trapezoidal footing is taken into consideration
Volume of Trapezoidal Footing (V) = V1 +V2
V1 = Squared Cubic Area
V2 =Truncated Pyramid Area
Let’s Find V2 ,
Top Square area = A2 = L2 x B2
= 0.720m x 0.70 m
=0.49 sq.mm
Bottom Square area = A1 = L1 x B1
= 1.6 m x 1.6 m
=2.56 sq.mm
V2 = (h/3) (A1 + A2 +√(A1 . A2))
= (0.5 / 3) x ( 0.49 + 2.56 + square root of ( 0.49 x 2.56))
= (0.1667) x (0.49 + 2.56 + 1.12)
= (0.1667) x ( 4.17 )
= 0.695 Cubic meter.
V2 = 0.695 m^{3}.
Let’s Find V1,
Square Cubic Area
V1 = L1 x B1 x H
= 1.5m x 1.5 m x 0.3 m
= 0.675 m^{3}.
Volume of Trapezoidal Footing V = V1 + V2 = 0.675 + 0.695 = 1.37 m^{3}
The formula can be used to get trapezoidal footing that’s either square or rectangle in dimension.
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shubham sharma says
it good information for me
Krunal Rajput says
Thanks