Correct Answer - Option 4 : 8 cm
Given:
The total surface area of the regular tetrahedron = 96√3 cm2
Formula used:
The total surface area of the regular tetrahedron = √3 × a2
The height of the tetrahedron = √6/3 × a
Where a is the side of the regular tetrahedron
Concept used:
The tetrahedron is a generally triangular pyramid
Calculation:
Let the side of the regular tetrahedron be a cm
As Surface area of regular tetrahedron = √3 × a2
⇒ √3 × a2 = 96√3
⇒ a = √96 = 4√6 cm
Now,
The height of the tetrahedron = √6/3 × a
⇒ √6/3 × 4√6
⇒ (6 × 4)/3
⇒ 8 cm
∴ The height of the regular tetrahedron is 8 cm
