Regular prism area

A prism is a polyhedron, two faces of which are congruent (equal) polygons lying in parallel planes, and the other faces are parallelograms that have common sides with these polygons. A straight prism is called regular if its bases are regular polygons.

The area of ​​a rectangular regular prism through its sides

Length of the side of the base of the prism а
Length of the side of the base of the prism b
Length of the side of the base of the prism c

Formulas for a rectangular prism:

  • Rectangular prism volume: V = abc
  • Surface area of ​​a rectangular prism: S = 2(ab + bc + ac)
  • Spatial diagonal of a rectangular prism: d = √(a2 + b2 + c2 (similarly the distance between points)

The cube is a special case where a= b = c. So you can find the surface area of ​​a cube by setting these values ​​equal to each other.

Calculations for a rectangular prism

1.Considering the length, width and height, find the volume, surface area and diagonal of a rectangular prism

  • a, b and c is known; find V, S and d
  • V = abc
  • S = 2(ab + bc + ca)
  • d = √(a2 + b2 + c2)

2. Knowing the surface area, length and width, find the height, volume and diagonal of a rectangular prism

  • S, b and а is known; find c, V and d
  • c = (S-2ab) / (2a + 2b)
  • V = abc
  • d = √(a2 + b2 + c2)

3. Knowing the volume, length, and width, find the height, surface area, and diagonal of a rectangular prism

  • V, a and b is known; find c, S and d
  • c = V / ab
  • S = 2(ab + bc + ac)
  • d = √(a2 + b2 + c2)

4. Knowing the diagonal, length and width, find the height, volume and surface area of ​​a rectangular prism

  • d, a and b is known; find с, V and S
  • h = √(d2-a2-b2)
  • V = abc
  • S = 2(ab + bc + ac)