Regular Octahedron Surface Area Calculator
Calculate the surface area of a regular octahedron by entering the edge length. A regular octahedron has 8 equilateral triangular faces.
💎 Regular Octahedron Surface Area
Formula
Regular Octahedron Formulas
Surface Area
Eight equilateral triangular faces
Triangle Area
Area of each equilateral triangular face
Volume
Volume of the octahedron
Height
Distance between opposite faces
Regular Octahedron Surface Area Examples
Example 1: Small Octahedron
Given: Edge length = 3 cm
Formula: SA = 2√3 × a²
Solution: SA = 2√3 × 3² = 2√3 × 9 = 18√3 ≈ 31.18 cm²
Example 2: Medium Octahedron
Given: Edge length = 5 cm
Formula: SA = 2√3 × a²
Solution: SA = 2√3 × 5² = 2√3 × 25 = 50√3 ≈ 86.60 cm²
Example 3: Large Octahedron
Given: Edge length = 8 cm
Formula: SA = 2√3 × a²
Solution: SA = 2√3 × 8² = 2√3 × 64 = 128√3 ≈ 221.77 cm²
Regular Octahedron Surface Area FAQ
What is a regular octahedron?
A regular octahedron is a 3D shape with 8 equilateral triangular faces, 12 edges, and 6 vertices. It's one of the five Platonic solids.
How do you calculate octahedron surface area?
Use the formula SA = 2√3 × a², where a is the edge length. This accounts for all 8 triangular faces.
Why is the formula 2√3 × a²?
Each triangular face has area (√3/4) × a². With 8 faces: 8 × (√3/4) × a² = 2√3 × a².
What are the properties of a regular octahedron?
It has 8 faces, 12 edges, 6 vertices. All faces are equilateral triangles, and all edges have the same length.