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
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)