# 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 = √(a**^{2}+ b^{2}+ c^{2 }(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 = √(a
^{2}+ b^{2}+ c^{2})

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 = √(a
^{2}+ b^{2}+ c^{2})

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 = √(a
^{2}+ b^{2}+ c^{2})

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 = √(d
^{2}-a^{2}-b^{2}) - V = abc
- S = 2(ab + bc + ac)