Pyramid with a Trapezoid Base

A pyramid is a building where the outer surfaces are triangular and converge at a point. The base of a pyramid can be trilateral, quadrilateral, or any polygon shape, meaning that a pyramid has at least three outer surfaces (at least four faces including the base). The square pyramid, with square base and four triangular outer surfaces, is a common version. (Source: Wikipedia)

I like to share this Trapezoid Shape with you all through my article.

Pyramid with trapezoid base:
      A pyramid with a trapezoid base is called as trapezoidal pyramid.
     Volume of trapezoidal pyramid = (1 / 3) * ((1 / 2) * (base₁ + base₂) * height

Example problems for pyramid with a trapezoid base

Trapezoid pyramid problem 1:
        A base length of the trapezoid pyramid is 12 cm, 14 cm and its height of the pyramid is 6 cm. Find the volume of the trapezoidal pyramid.
Solution:
     Given base lengths are b₁ = 12 cm, b₂ = 14 cm, and h = 6 cm.
Formula:
   Volume of trapezoidal pyramid = (1 / 3) * ((1 / 2) * (base₁ + base₂) * height
Substitute the given values in the above formula, we get
= (1 / 3) * ((1 / 2) * (12 + 14) * 6 cm³
= (1 / 3) * 78 cm³
= 26 cm³

Answer:
 Volume of the trapezoidal pyramid is 26 cm³

Trapezoid pyramid problem 2:
        A base length of the trapezoid pyramid is 15 cm, 24 cm and its height of the pyramid is 9 cm. Find the volume of the trapezoidal pyramid.
Solution:
     Given base lengths are b₁ = 15 cm, b₂ = 24 cm, and h = 9 cm.
Formula:
Volume of trapezoidal pyramid = (1 / 3) * ((1 / 2) * (base₁ + base₂) * height
 Substitute the given values in the above formula, we get
= (1 / 3) * ((1 / 2) * (15 + 24) * 9 cm³
 = (1 / 3) * 175.5 cm³
                                               = 58.5 cm³
Answer:
 Volume of the trapezoidal pyramid is 58.5 cm³

Trapezoid pyramid problem 3:
        A base length of the trapezoid pyramid is 6 cm, 11 cm and its height of the pyramid is 5 cm. Find the area of the trapezoid.
Solution:
     Given base lengths are b₁ = 6 cm, b₂ = 11 cm, and h = 5 cm.
Formula:
Area of trapezoid = ((1 / 2) * (base₁ + base₂) * height
Substitute the given values in the above formula, we get
                                               = (1 / 2) * (6 + 11) * 5 cm³
                                               = (1 / 2) * 85 cm³
                                               = 42.5 cm²
Answer:
 Volume of the trapezoidal pyramid is 42.5 cm²

Practice problems for pyramid with a trapezoid base

Trapezoid pyramid problem 1:
        A base length of the trapezoid pyramid is 7 cm, 9 cm and its height of the pyramid is 12 cm. Find the volume of the trapezoidal pyramid.
Answer:
 Volume of the trapezoid pyramid is 32 cm³
Trapezoid pyramid problem 2:
        A base length of the trapezoid pyramid is 10 cm, 22 cm and its height of the pyramid is 7 cm. Find the volume of the trapezoidal pyramid.
Answer:

 Volume of the trapezoid pyramid is 37.33 cm³