Solid Geometry

Prisms

Right triangular prism

Prism
A prism is a polyhedron (having five or more faces) with two parallel and congruent polygonal bases, so that all cross-sections taken parallel to the bases are also congruent with the bases, thus all lateral faces (sides) are parallelograms.
Lateral faces meet in line segments called lateral edges.
A right prism is one whose lateral faces and lateral edges are perpendicular to its bases. The lateral faces of a right prism are all rectangles, and the height of a right prism is equal to the length of its lateral edge.
A regular prism has regular polygons as bases. A regular polygon is one that has all sides equal in length and all angles equal in measure.
Thus, a right regular prism is one with regular polygon bases and perpendicular rectangular lateral sides.
 S = 2B + Slat - surface of a prism Slat = P · h - lateral surface V = B · h - volume of a prism B -area of base,  P - perimeter of base,  h -height of a prism
Cube
A solid with six identical square faces that are mutually perpendicular.
 - diagonal S = 2B + Slat = 2a2 + 4a2 = 6a2 - surface V = B · h = a2 · a = a3 - volume
Rectangular prism or rectangular parallelepiped (cuboid)
A solid of which the six faces are mutually perpendicular rectangles is called a rectangular parallelepiped or a rectangular prism.
 - diagonal S = 2B + Slat = 2(ab + ac + bc) - surface V = B · h = a · b · c - volume
Right triangular prism
A right triangular prism is made of two triangular bases and three rectangular faces with lateral edges perpendicular to the bases.
 S = 2B + Slat =  a ha + (a + b + c)· h - surface V = B · h = 1/2 · a ha · h - volume
Regular right triangular prism
A prism made of two equilateral triangular bases and three identical rectangular sides is called a regular right triangular prism.
 - surface - volume
Regular right hexagonal prism
A prism made of two regular hexagonal bases and six identical rectangular sides is called a regular right hexagonal prism.
 - surface - volume