Lateral Area

Lateral area is the surface area of a 3D solid excluding its base or bases, measured in square units. It covers the side walls only, the relevant quantity when the bases are not part of the visible surface (the wall of a tank, the curved sheet of a cone). The formulas below cover right prisms, cylinders, pyramids, and cones.

Right Prism

Base perimeter P and prism height h. The side walls unroll into a single rectangle of width P and height h:

Whare

P = Perimeter of the base

h = height of the prism

cylinder

The circular case of a right prism, with base perimeter 2πr. Base radius r and height h. Unrolling the curved side gives a rectangle of width 2πr and height h:

Where

r = radius of the base

h = geight of the cylinder

Pyramid

Base perimeter P and slant height l (the distance from the apex down the face to the midpoint of a base edge, not the perpendicular height). Lateral area is half the base perimeter times the slant height. The one-half factor matches a triangle’s area-to-base-times-height ratio:

Where

P = Perimeter of base

l = slant height

Cone

Base radius r and slant height l (apex to base-edge along the surface, not the vertical axis). The circular case of the pyramid rule. Unrolled, the surface is a circular sector of radius l whose arc length matches the base circumference:

Where

r = radius of it’s base

l = slant height of the cone