The volume of a prism

Volume is a number measuring how much space a solid takes: every solid has a positive volume, equal solids have equal volumes, if a solid is cut into pieces its volume is the sum of the pieces’ volumes, and the unit cube of edge 1 has volume 1. Units: 1 m³ = 1000 dm³ = 1,000,000 cm³, and 1 dm³ = 1 litre. The volume of a cuboid is V = a · b · c, hence V = S_base · h. It is proved that for every parallelepiped and every prism V = S_base · h: a right triangular prism is doubled to a cuboid, any right prism is handled by splitting its base into triangles, and an oblique prism has the same volume as the right prism with the same base and height (the height is the perpendicular distance between the bases, h = l · sin α, where l is the lateral edge and α its angle with the base). Solids with equal volumes are called equivalent; they need not be congruent. In problems find the base area first and then the height.