Surface Area of 3D Figures

General Approach to Finding Surface Area

• Calculate the base area (B) and the lateral surface area (LSA) separately.

• Add them together to find the total surface area (TSA).

Rectangular Prism

• Perimeter of the base: $P = 2(l + w)$

• Area of the base: $B = lw$

• Lateral surface area: $LSA = Ph$

• Total surface area: $TSA = 2B + LSA$

Triangular Prism

• Perimeter of the base: $P = a + b + c$

• Area of the base: $B = \frac{1}{2}bh$

• Lateral surface area: $LSA = Pl$

• Total surface area: $TSA = 2B + LSA$

Cylinder

• Circumference of the base: $C = 2\pi r$

• Area of the base: $B = \pi r^2$

• Lateral surface area: $LSA = Ch$

• Total surface area: $TSA = 2B + LSA$

Sphere

• A sphere does not have a separate base.

• Total surface area: $TSA = 4\pi r^2$

Square Pyramid

• Perimeter of the base: $P = 2l + 2w$

• Area of the base: $B = lw$

• Lateral surface area: $LSA = \frac{1}{2}Ps$, where s is the slant height (the height of the triangular side).

• Total surface area: $TSA = B + LSA$

Cone

• Perimeter of the base: $P = 2\pi r$

• Area of the base: $B = \pi r^2$

• Lateral surface area: $LSA = \pi rs$, where s is the slant height.

• Total surface area: $TSA = B + LSA$

Note on Lateral Surface Area of a Cone

• The formula $LSA = \pi rs$ can be derived from the net of the cone and the sector area formula.