Surface Area of a Solid
The sum of the areas of all the faces of a solid.
The following distinction is made between the lateral area and the total area of a solid:
- Lateral area of a solid: The sum of the areas of the lateral faces of some solids.
- Total area of a solid: The sum of the areas of all the faces of a solid, including the bases, if applicable.
Formulas
| Solids | Lateral area [latex]A_l[/latex] | Total area [latex]A_t[/latex] | Nomenclature |
Cube
 |
[latex]A_l=4c^2[/latex] | [latex]A_t=6c^2[/latex] | c: length of an edge of the cube |
Rectangular prism
 |
[latex]A_l=2×(ac + bc)[/latex] | [latex]A_t=2×(ab+ac+bc)[/latex] | a: length b: width c: height |
Right circular cylinder
 |
[latex]A_l=2\pi rh[/latex] | [latex]A_t=2\pi r^2+2\pi rh[/latex] | r: radius h: height |
Regular pyramid
 |
[latex]A_l=\frac{nca}{2}[/latex] | [latex]A_t=A_b+\frac{nca}{2}[/latex] | Ab: area of the base c: side length of the base n: number of sides of the base a: slant height |
Right circular cone
 |
[latex]A_l=\frac{\pi da}{2}[/latex] ou [latex]A_l=\pi ra[/latex] | [latex]A_t=\pi r^2+\pi ra[/latex] | a: slant height r: radius h: height where a² = h² + r² |
Sphere
 |
[latex]A_l=4\pi r^2[/latex] | [latex]A_t=4\pi r^2[/latex] | r: radius of the sphere |