Identify the shape and its dimensions
Determine which faces make up the surface
Find the area of each face (use the correct formula for each face)
Add all face areas together to get total surface area
Common formulas
Rectangle: (A=lw)
Square: (A=s^2)
Triangle: (A=tfrac12 bh)
Circle: (A=pi r^2)
Parallelogram: (A=bh)
Trapezoid: (A=tfrac12 (b_1+b_2)h)
Regular polygon (perimeter method): (A=tfrac12 aP) where (a) is apothem and (P) is perimeter
Surface area of prisms
Total surface area: (SA=2B+Ph)
(B) = area of base, (P) = perimeter of base, (h) = height
Surface area of cylinders
Total surface area: (SA=2pi r^2+2pi rh)
Lateral area only: (LA=2pi rh)
Surface area of pyramids
Total surface area: (SA=B+tfrac12 Pl)
(B) = base area, (P) = base perimeter, (l) = slant height
Surface area of cones
Total surface area: (SA=pi r^2+pi rl)
Lateral area only: (LA=pi rl)
Surface area of spheres
Total surface area: (SA=4pi r^2)
Lateral area only (when needed)
Prism: (LA=Ph)
Pyramid: (LA=tfrac12 Pl)
Cylinder: (LA=2pi rh)
Cone: (LA=pi rl)
Sphere: no separate lateral area (full surface)