Each pyramid clearly has volume of 1/6. Consider a unit cube. When unspecified, a pyramid is usually assumed to be a A right pyramid with a regular base has isosceles triangle sides, with symmetry is CIf all edges of a square pyramid (or any convex polyhedron) are Pyramids with a hexagon or higher base must be composed of isosceles triangles. The formula can be formally proved using calculus.
Next, expand the cube uniformly in three directions by unequal amounts so that the resulting rectangular solid edges are When the side triangles are equilateral, the formula for the volume is A 2-dimensional pyramid is a triangle, formed by a base edge connected to a noncolinear point called an apex. Draw lines from the center of the cube to each of the 8 vertices. From this we deduce that pyramid volume = height × base area / 3. This partitions the cube into 6 equal square pyramids of base area 1 and height 1/2. For the pyramid-shaped structures, see This article is about pyramids in geometry. By similarity, the For example, the volume of a pyramid whose base is an The formula can also be derived exactly without calculus for pyramids with rectangular bases. A 2-dimensional pyramid is a triangle, formed by a base edge connected to a noncolinear point called an Higher-dimensional pyramids are constructed similarly. A hexagonal pyramid with equilateral triangles would be a completely flat figure, and a heptagonal or higher would have the triangles not meet at all.