Question
If the lateral surface area of a regular tetrahedron is
108√3 cm², what is its volume?Solution
ATQ,
Let the length of edge of the tetrahedron be 's' cm
Lateral surface area of a tetrahedron = 3 × (√3/4) × s²
ATQ;
108√3 = 3 × (√3/4) × s²
Or, s² = 144
So, s = 12 (Since, length cannot be negative therefore we will take the positive root only)
Volume of tetrahedron = (√2/12) × s³
= (√2/12) × 12 × 12 × 12
= 144√2 cm³
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