Identify the shape of the surface (cube, rectangular prism, cylinder, sphere, cone, pyramid, etc.).
Determine the needed dimensions (e.g., side lengths, radius, height).
Use the correct surface-area formula for the shape:
Cube (side s): (6s^2)
Rectangular prism (length l, width w, height h): (2(lw + lh + wh))
Square pyramid (base side b, slant height s): (b^2 + 2bs)
Rectangular pyramid (base l×w, slant heights (s_1, s_2)): (lw + ls_1 + ws_2)
Cylinder (radius r, height h): (2pi r^2 + 2pi rh)
Cone (radius r, slant height s): (pi r^2 + pi rs)
Sphere (radius r): (4pi r^2)
Hemisphere (radius r): (3pi r^2) (curved only: (2pi r^2))
Triangular prism (triangle sides a, b, c; triangle area A; length L): (2A + L(a+b+c))
General composite surfaces: add the areas of all faces/sides and subtract overlapping/hidden areas if required
For slant height on pyramids/cones, compute from given dimensions when needed:
Right square pyramid: (s=sqrt{(b/2)^2+h^2})
Right circular cone: (s=sqrt{r^2+h^2})
Substitute values into the formula.
Use consistent units for all dimensions.
Evaluate and simplify the result.
If a problem requests rounding, round to the specified number of decimal places.
Report the final answer in square units (e.g., (text{cm}^2), (text{m}^2)).