# Volume of a Trapezoid

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A trapezoid is a 2-dimensional geometric figure which has one pair of parallel sides and one pair of non-parallel sides. We can calculate the area and the perimeter of a trapezoid but it is not possible to calculate the volume of a trapezoid because we need 3 dimensions to find the volume and a trapezoid does not have 3 dimensions. However, a trapezoidal prism consists of congruent trapezoidal bases and we can find the volume of this prism because it is a 3-dimensional structure.

Example 1: Calculate the volume of a trapezoidal prism whose parallel sides of base trapezoid are 3m and 6m, height of the base is 4m andlength of the prism is 8m

Given: length of the base parallel sides ==> a= 3m and b= 6m

Height of the base trapezoid, h = 4m

Length of the prism, l = 8m

Volume of a trapezoidal prism, V = 1/2 *(a + b)* h * l

This gives, volume, V= 1/2* 9m* 4m* 8m= 144m3

Therefore, volume of the given trapezoidal prism is 144m3

Example 2: Calculate the volume of a trapezoidal prism whose parallel sides of base trapezoid are 4m and 7m, height of the base is 5m and length of the prism is 10m.

Given: length of the base parallel sides ==> a= 4m and b= 7m

Height of the base trapezoid, h = 5m

Length of the prism, l = 10m

Volume of a trapezoidal prism, V = 1/2 *(a + b)* h * l

This gives, volume, V= 1/2* 11m* 5m* 10m= 275m3

Therefore, volume of the given trapezoidal prism is 275m3