lesson
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Imagine you are wrapping a label around a soup can or painting the four walls of your bedroom without touching the floor or ceiling.
The area of just those surrounding side faces is called the lateral surface area, which leaves out the top and bottom bases entirely.
πA clean 3D isometric diagram of a standing rectangular prism. The top and bottom faces (bases) are light gray (#e2e8f0) with clear dotted outlines labeled 'Base (excluded)'. The four vertical side walls are highlighted in bright cyan-blue (#0ea5e9) with translucent shading and labeled 'Lateral Faces'. Clean modern typography, soft drop shadows, white background card (#ffffff), rounded 12px corners.
What happens if you slice along one vertical edge and unfold all the side walls onto a flat table?
Why the Formula Works
A prism is a 3D solid with two congruent, parallel polygons called bases connected by rectangular side faces.
When you unfold the lateral faces flat, they align side-by-side to form one giant rectangle.
πAn interactive or step-by-step visual unfolding of a triangular prism. Step 1 shows the 3D triangular prism with base side lengths a, b, c and height h. Step 2 shows the 3 lateral rectangles unrolling flat into a single long rectangle. The top edge of the rectangle shows segments labeled 'a', 'b', and 'c' totaling 'Perimeter P = a + b + c'. The vertical edge is labeled 'Height h'. The total area is labeled 'L = P Γ h'. Vibrant colors: blue accents (#0ea5e9), dark text (#1e2945).
The length of this giant rectangle is the distance all the way around the base, known as the base perimeter (P), and its width is the prism's height (h).
Since the area of any rectangle is length times width, the lateral area formula is simply L=Ph.
How do we apply this formula when the base is a simple rectangle?
Example 1: Rectangular Prism
Find the lateral surface area of a box with a base measuring 8Β cm by 5Β cm and a height of 12Β cm.