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

If the total surface area of the regular tetrahedron is 144√3 cm2, then what is the lateral surface area of the regular tetrahedron? Correct Answer 108√3 cm<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em; font-size:10.5px;">2</span>

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 

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