Volume Formulas for Rectangular and Triangular Prisms

Volume of Rectangular Prisms (Cuboids)

• A rectangular prism, also referred to as a cuboid, is a three-dimensional solid shape bounded by six rectangular faces.
• Key dimensional variables:
  • $l$ represents the length of the base.
  • $w$ (or $W$) represents the width of the base.
  • $h$ represents the perpendicular height of the prism.
• General formula for volume:
  • The volume ($V$) is obtained by multiplying the area of the base ($A$) by the perpendicular height:
  • $V = A \times \text{perp. height}$
  • Substituting the area of the rectangular base ($A = l \times w$):
  • $V = l \times w \times h$
  • $V = l w h$

Volume of Triangular Prisms

• A triangular prism is a three-dimensional polyhedron bounded by two identical triangular bases and three rectangular side faces.
• Key dimensional variables:
  • $b$ represents the base edge of the triangular face.
  • $h_1$ represents the perpendicular height of the triangular face.
  • $h_2$ represents the overall perpendicular height (length) of the prism.
• General formula for volume:
  • The volume ($V$) is calculated by multiplying the area of the triangular cross-section ($A$) by the perpendicular height of the prism:
  • $V = A \times \text{perp. height}$
  • Area of the triangular base ($A$):
  • $A = \frac{1}{2} \times b \times h_1$
  • Complete volume formula for a triangular prism:
  • $V = \left(\frac{1}{2} \times b \times h_1\right) \times h_2$