Table of Content

• What is Tetrahedron?
• How to Find Volume of a Tetrahedron
• Tetrahedron Volume Formula
• Tetrahedron Volume Formula When Four Points are Given
• Regular Tetrahedron Formula
• Examples on Volume of Tetrahedron

Area of One Face of Regular Tetrahedron Formula	A = 1/4√(3)a2
Total Surface Area of Regular Tetrahedron Formula	A = a2√(3)
Slant Height of a Regular Tetrahedron Formula	l = a√(3/2)
Altitude of a Regular Tetrahedron Formula	h = a√(6)/3
Volume of a Regular Tetrahedron Formula	V = a3√(2)/12

Read More:

• Area Formulas
• Tetrahedron Formulas
• Volume Formulas for 3D Shapes

Examples on Volume of Tetrahedron

Example 1: Find the volume of the tetrahedron with edge 6 units.

Solution:

Volume of tetrahedron is given by:

Volume of Tetrahedron = a³ / (6√2)

Volume of tetrahedron = 6³ / (6√2)

= 36 / (√2)

= 18√2 cubic units.

Example 2: If edge of the tetrahedron is 4 units then, find the volume of tetrahedron.

Solution:

Volume of tetrahedron is given by:

Volume of Tetrahedron = a³/(6√2)

Volume of tetrahedron = 4³ / (6√2)

= 64/ (6√2)

= 32 / (3√2)

= (16√2) / 3 = 7.54 cubic units

Example 3: Find the edge of the tetrahedron if the volume of tetrahedron given is 144√2 cubic units.

Solution:

Volume of tetrahedron is given by:

Volume of Tetrahedron = a³/(6√2)

a³ = Volume of tetrahedron × 6√2

a³ = 144√2 × 6√2

a³ = 1728

a = ∛1728

a = 12 units

Therefore, the edge of given tetrahedron is 12 units.

Practice Problems on Volume of Tetrahedron

Q1. Find the volume of the tetrahedron with edge 18 units.

Q2. If edge of the tetrahedron is 9 units then, find the volume of tetrahedron.

Q3. Find the edge of the tetrahedron if the volume of tetrahedron given is 52 cubic units.

FAQs on Volume of Tetrahedron

What is Formula for a Tetrahedron?

Regular Tetrahedron Formula

Area = √3x² (x is Side Length)

How to Calculate Volume of a Tetrahedral?

Volume of tertahedral is calculated using volume of terahedral formula as discussed in the article.

What is Surface Area of a Tetrahedron?

Total Surface Area of Regular Tetrahedron Formula: A = a²√(3).

What is Perimeter of a Tetrahedron?

Perimeter of any regular terahedron with side a is, P = 6a units.

What is Formula for Volume of a Tetrahedron?

Formula for volume of tetrahedron is given by:

Volume of Tetrahedron = a³ / (6√2)

What is Volume of a Tetrahedron Given 4 Points?

Volume of a tetrahedron given 4 points is calculated using formula:

Volume of Tetrahedron = (1/6) × Scalar Product of Three Vectors determined from Given 4 Points