Question
A regular tetrahedron has a lateral surface area of 108√3
cm². Calculate its volume.Solution
ATQ,
Let the edge length of the tetrahedron be 's' cm
Lateral surface area = 3 × (√3/4) × s²
As given,
108√3 = 3 × (√3/4) × s²
⇒ s² = 144
⇒ s = 12
Volume = (√2/12) × s³
= (√2/12) × 12 × 12 × 12
= 144√2 cm³
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