Volume of Prisms

Geometry · Axiom Academy

Base area times height — the one formula that measures every prism. Picture making a copy of the base and stacking those copies straight up. Each layer contributes its area B , so stacking it to a height h sweeps out the whole solid. The volume is just the base area carried through the height. The formula V = Bh never changes — only the recipe for the base area B does. Watch the same prism keep one height while its base swaps between a rectangle, a triangle, and a square — each time we recompute B and reapply V = Bh. Find the volume of a rectangular prism with length 8 cm , width 5 cm , and height 6 cm . A triangular prism has a triangular base with base 6 m and height 4 m . The prism's length is 10 m . Find the volume. Step 1 — area of the triangular base Step 2 — multiply by the prism's length 5. Finding a Missing Dimension The formula works backwards too. A rectangular prism has volume 180 in³ , length 9 in , and width 4 in . Find the height. Watch the base stay fixed while the height grows — the volume fills up until it hits 180, and that's where the height locks in. Every prism, no matter the base, is measured the same way: find the base area, carry it through the height. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Geometry course.