Triangular Prism Volume

A triangular prism is a triangle extruded along a straight line: a tent, a gable roof space, a wedge of cheese, a section of dredged spoil. Its volume is the triangular end area $\tfrac{1}{2}bh_t$ multiplied by the run $L$. The subscript matters, because $h_t$ is the height of the triangle, measured perpendicular to its base, and has nothing to do with how tall the prism stands.

The formula is worth knowing for the attic. A house 10 m long with a gable 8 m wide rising 3 m to the ridge encloses $\tfrac{1}{2}(8)(3)(10) = 120$ m³ of air, which is exactly the number an insulation contractor or a ventilation designer needs. A handy check on your work: a 3-4-5 right triangle has area exactly 6, so any prism built on one should come out as six times its length.