🔺 Triangular Pyramid Surface Area Calculator
Calculate Surface Area of Tetrahedrons
Total Surface Area, Lateral Area & Volume
Triangular Pyramid Surface Area Calculator
⬡ Regular Tetrahedron (All Edges Equal)
📊 Calculation Breakdown
Triangular Pyramid Surface Area Formulas
Regular Tetrahedron (All Edges Equal)
Where a = edge length. All 4 faces are identical equilateral triangles.
General Triangular Pyramid
Sum of base area plus all three lateral face areas.
Base Area (Heron's Formula)
Where s = (a+b+c)/2 is the semi-perimeter.
Volume
Where h is the perpendicular height from base to apex.
Regular Tetrahedron Height
Types of Triangular Pyramids
| Type | Description | Faces | Special Properties |
|---|---|---|---|
| Regular Tetrahedron | All 6 edges equal | 4 equilateral triangles | Highly symmetric, Platonic solid |
| Right Triangular Pyramid | Apex directly above base centroid | 1 base + 3 congruent lateral | Perpendicular height meets base center |
| Oblique Triangular Pyramid | Apex not above base center | 4 different triangles | No axis of symmetry |
| Isosceles Tetrahedron | Opposite edges equal | 4 congruent triangles | All faces have equal area |
How to Calculate Triangular Pyramid Surface Area
- Identify the pyramid type — Determine if it's regular (all edges equal) or irregular.
- Measure the base — Find all three sides of the triangular base.
- Calculate base area — Use Heron's formula: A = √(s(s-a)(s-b)(s-c)).
- Find lateral face areas — Calculate or measure each of the three lateral triangles.
- Sum all areas — Total SA = Base Area + Lateral Face 1 + Face 2 + Face 3.
Educational Resources
Frequently Asked Questions
A triangular pyramid (tetrahedron) is a 3D solid with a triangular base and three triangular lateral faces meeting at an apex. It has 4 faces, 6 edges, and 4 vertices — the simplest type of pyramid.
A regular tetrahedron is a triangular pyramid where all 6 edges have equal length, making all 4 faces identical equilateral triangles. It's one of the five Platonic solids with the highest symmetry.
Total SA = Base Area + Face 1 + Face 2 + Face 3. For a regular tetrahedron: SA = √3 × a², where a is the edge length.
Use Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 is the semi-perimeter. For equilateral triangles, use A = (√3/4) × side².
Total surface area includes all 4 faces (base + 3 lateral faces). Lateral surface area includes only the 3 triangular side faces, excluding the base.
A triangular pyramid has exactly 4 faces: 1 triangular base and 3 triangular lateral faces. It also has 6 edges and 4 vertices.
For a regular tetrahedron with edge length a, the height is: h = a × √(2/3), which simplifies to approximately h ≈ 0.8165 × a.
Slant height is the distance from the apex to the midpoint of a base edge, measured along a lateral face. It's different from the perpendicular height (apex to base center).
Tetrahedrons appear in: molecular geometry (methane CH₄), architecture (tetrahedral trusses), gaming dice (D4), crystals, and packaging (Tetra Pak).
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Last Updated: January 2026