Volume of Triangular Prisms
Volume of triangular prisms is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume. The volume formula is V equals one-half times base times triangle height times prism height, because the triangular base area requires the one-half factor. A common error is forgetting the one-half factor, which doubles the correct answer.
Key Concepts
For a triangular prism, $V = B \cdot h$ where $B = \frac{1}{2} \cdot b \cdot h {triangle}$ and $h$ is the prism height.
$$V = \frac{1}{2} \cdot b \cdot h {triangle} \cdot h {prism}$$.
Common Questions
What is the formula for the volume of a triangular prism?
The volume of a triangular prism is V equals one-half times b times h_triangle times h_prism, where b is the triangle base, h_triangle is the triangle height, and h_prism is the length of the prism.
Why do you multiply by one-half when finding the volume of a triangular prism?
Because the cross-section is a triangle, and the area of a triangle is one-half times base times height. The volume is this triangular base area multiplied by the prism length.
What is the most common mistake when calculating triangular prism volume?
The most common error is forgetting the one-half factor for the triangular base area, which results in an answer twice as large as the correct volume.
What textbook covers triangular prism volume in Grade 7?
Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume covers the volume of triangular prisms and other 3D figures.