# Surface Area of a Solid

## 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 $$A_l$$ 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