If the total surface area of the regular tetrahedron is 96√3 cm2, th

1.	If the total surface area of the regular tetrahedron is 96√3 cm2, then what is its height?1. 5 cm 2. 7 cm3. 6 cm4. 8 cm
Answer» 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

If the total surface area of the regular tetrahedron is 96√3 cm2, then what is its height?1. 5 cm 2. 7 cm3. 6 cm4. 8 cm

Answer» 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

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