Lateral Surface Area

High School

Definition

The surface area of 3D objects without its top and bottom base. The surface area is found by finding the area of the individual faces of an object and then summing it together to find the total surface area. In order to find just the lateral area, do not sum up the areas of the top and bottom base when totalling up the surface area.

Worked examples

\(\)Rectangular prism: \( L = 2lh + 2wh\)

Lateral area is the four vertical faces only — two pairs of rectangles — excluding the top and bottom bases.

\(\)Cylinder: \( L = 2\pi rh\)

The curved side unrolls into a rectangle; the two circular bases are not part of the lateral area.

\(\)Square pyramid: \( L = 4 \times \frac{1}{2}bs = 2bs\)

Sum the four triangular faces; the square base is excluded from lateral surface area.

Common mistakes

\(\)Cylinder: \( L = 2\pi rh + 2\pi r^2\) → \(L = 2\pi rh\) Lateral area excludes the top and bottom circular bases; \(2\pi r^2\) is for the bases only.
\(\)Prism: \( L = 2lw + 2lh + 2wh\) → \(L = 2lh + 2wh\) The \(2lw\) term is the top and bottom bases, which are not lateral faces.
For a cone, including the circular base in lateral area → Cone lateral area is \(L = \pi r\ell\) (slant height only) The base circle is excluded; only the slanted surface counts as lateral.

Where you'll use it next

You'll use lateral surface area to find the material needed to wrap cylinders and prisms, in optimization problems in precalculus, and in surface integrals in multivariable calculus.

Found in 1 StudyPug lesson

Surface Area of Prisms: Mastering Calculations and Formulas

Grade 8 Math

Dive into the world of prism surface areas! Learn essential formulas, step-by-step calculations, and real-world applications. Perfect for students looking to excel in geometry and problem-solving.

8th Grade8th