Enter the perimeter of the base and the height of the prism into the calculator to determine the lateral area. This calculator can also evaluate any of the variables given the others are known.
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Lateral Area of Prism Formula
The following formula calculates the lateral area of a right prism.
LA = P * h
Variables:
- LA is the lateral area (square units) – the total area of all side faces, excluding both bases
- P is the perimeter of the base (units) – the sum of all edge lengths of the base polygon
- h is the height of the prism (units) – the perpendicular distance between the two base faces
This formula applies to right prisms only. In an oblique prism, the lateral faces are parallelograms rather than rectangles, and each face must be computed individually using its slant height.
Lateral Area by Prism Type
The formula LA = P x h is universal, but the base perimeter calculation differs by shape. Geometrically, unrolling the lateral surface of any right prism produces a single rectangle with width equal to the base perimeter and height equal to the prism height. This is why the formula holds regardless of the number of base sides.
| Prism Type | Base Perimeter (P) | Lateral Area Formula | Lateral Faces |
|---|---|---|---|
| Rectangular | 2(l + w) | 2h(l + w) | 4 |
| Square | 4s | 4sh | 4 |
| Triangular | a + b + c | (a + b + c)h | 3 |
| Regular Pentagonal | 5s | 5sh | 5 |
| Regular Hexagonal | 6s | 6sh | 6 |
| Regular n-sided | n x s | n x s x h | n |
Lateral Area vs Total Surface Area
Lateral area covers only the side faces. Total surface area (TSA) adds both base faces:
TSA = LA + 2B
Where B is the area of one base. Use lateral area when computing paint for walls (floor and ceiling excluded), pipe or column cladding, or the label area of a rectangular box.
Reference: Lateral Area for Common Rectangular Prism Dimensions
Pre-calculated lateral areas for standard real-world rectangular prism dimensions (all values rounded):
| Object / Room | L x W x H | Base Perimeter | Lateral Area |
|---|---|---|---|
| Small room | 3 m x 3 m x 2.4 m | 12 m | 28.8 m² |
| Standard bedroom | 4 m x 3.5 m x 2.4 m | 15 m | 36.0 m² |
| Large room | 5 m x 4 m x 2.4 m | 18 m | 43.2 m² |
| Shipping box (small) | 30 cm x 20 cm x 15 cm | 100 cm | 1,500 cm² |
| Shipping box (medium) | 60 cm x 40 cm x 30 cm | 200 cm | 6,000 cm² |
| Standard brick | 21.5 cm x 10.2 cm x 6.5 cm | 63.4 cm | 412 cm² |
What is the Lateral Area of a Prism?
The lateral area of a prism is the total area of its side faces, the panels connecting the two congruent base polygons. It excludes both bases. The lateral area scales linearly with both perimeter and height: doubling either dimension doubles the lateral area. For a fixed base perimeter, a prism with more sides approaches a cylinder, and its lateral area converges to 2 x pi x r x h.
How to Calculate Lateral Area of a Prism
- Determine the perimeter of the base (P) by summing all base edge lengths.
- Determine the height of the prism (h), the perpendicular distance between the two bases.
- Apply the formula: LA = P x h.
Example: Shipping Box
A rectangular shipping box measures 30 cm x 20 cm x 15 cm. How much material covers the four sides (excluding top and bottom flaps)?
- Base perimeter: P = 2(30 + 20) = 100 cm
- Height: h = 15 cm
- Lateral area: LA = 100 x 15 = 1,500 cm²
- Total surface area: TSA = 1,500 + 2(30 x 20) = 1,500 + 1,200 = 2,700 cm²
