Surface Area of a Rectangular Prism Calculator
Calculate total surface area, lateral area, and volume of rectangular prisms with step-by-step solutions
Calculate Rectangular Prism Properties
First base edge length
Second base edge length
Lateral edge length (prism height)
Rectangular Prism Formulas
Base Area: A_b = l × w
Lateral Area: A_l = 2(lh + wh) = 2h(l + w)
Total Surface Area: A = 2A_b + A_l = 2lw + 2lh + 2wh
Volume: V = l × w × h
Space Diagonal: d = √(l² + w² + h²)
Example Calculations
Example 1: Shipping Box
Given: l = 8 ft, w = 6 ft, h = 5 ft
Base area: 8 × 6 = 48 ft²
Lateral area: 2(8×5 + 6×5) = 140 ft²
Total area: 2×48 + 140 = 236 ft²
Example 2: Swimming Pool
Given: l = 10 m, w = 4 m, h = 2 m
Base area: 10 × 4 = 40 m²
Lateral area: 2(10×2 + 4×2) = 56 m²
Total area: 2×40 + 56 = 136 m²
Quick Reference
Key Formulas
A = 2lw + 2lh + 2wh
A_l = 2h(l + w)
V = lwh
d = √(l² + w² + h²)
Components
6 rectangular faces
2 bases (top & bottom)
4 lateral faces
12 edges, 8 vertices
Rectangular Prism Facts
Quick Tips
Also called a cuboid or rectangular box
Total surface area includes all 6 faces
Lateral area excludes top and bottom faces
Space diagonal connects opposite vertices
Understanding Rectangular Prism Surface Area
What is a Rectangular Prism?
A rectangular prism (also called a cuboid) is a 3D shape with six rectangular faces. Think of a shoebox, shipping container, or any rectangular box. All angles are right angles (90°), and opposite faces are identical rectangles.
Surface Area Components
The surface area consists of all six faces: two identical bases (top and bottom) and four lateral faces. The lateral faces form the "sides" of the prism.
Formula Derivation
Step 1: Base Areas
Two bases: 2 × (l × w) = 2lw
Step 2: Lateral Areas
Four sides: 2(lh) + 2(wh) = 2h(l + w)
Step 3: Total Area
A = 2lw + 2lh + 2wh
Real-World Applications
Construction:
Calculate material needed for walls, floors, and ceilings of rectangular rooms
Packaging:
Determine wrapping paper or paint needed for boxes and containers
Swimming Pools:
Calculate tiling area for rectangular pools (excluding top surface)