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 \(A_l\) |
Total area \(A_t\) |
Nomenclature |
Cube |
\(A_l=4c^2\) | \(A_t=6c^2\) | c: length of an edge of the cube |
Rectangular prism |
\(A_l=2×(ac + bc)\) | \(A_t=2×(ab+ac+bc)\) | a: length b: width c: height |
Right circular cylinder |
\(A_l=2\pi rh\) | \(A_t=2\pi r^2+2\pi rh\) |
r: radius h: height |
Regular pyramid |
\(A_l=\frac{nca}{2}\) | \(A_t=A_b+\frac{nca}{2}\) | Ab: area of the base c: side length of the base n: number of sides of the base a: slant height |
| Right circular cone
|
\(A_l=\frac{\pi da}{2}\) ou \(A_l=\pi ra\) |
\(A_t=\pi r^2+\pi ra\) | a: slant height r: radius h: height where a² = h² + r² |
| Sphere
|
\(A_l=4\pi r^2\) | \(A_t=4\pi r^2\) | r: radius of the sphere |
