Question

If the total surface area of the regular tetrahedron is 144√3 cm², then what is the lateral surface area of the regular tetrahedron?

1. 118√3 cm2
2. 128√3 cm2
3. 136√3 cm2
4. 108√3 cm2

Answer 1

Correct Answer - Option 4 : 108√3 cm2

Given:

The total surface area of the regular tetrahedron = 144√3 cm2

Formula Used:

The total surface area of the regular tetrahedron = √3 × a2

The lateral surface area of the regular tetrahedron = (3√3 × a2)/4

Where a is the side of the regular tetrahedron

Calculation:

The total surface area of the regular tetrahedron = 144√3 cm2

⇒ √3 × a2 = 144√3

⇒ a2 = 144

⇒ a = √144

⇒ a = 12 cm

The lateral surface area of the regular tetrahedron = (3√3 × a2)/4

⇒ 3√3 × (12)2/4

⇒ 3√3 × 144/4

⇒ 3√3 × 36

⇒ 108√3 cm2

∴ The lateral surface area of the regular tetrahedron is 108√3 cm2