All edges of a square pyramid are of the same length and its height is 12 centimetres. What is its volume?

Let all the edges of the square prism be 'a'.

The lateral edge BC is also 'a'.

HL = height of pyramid

HG = half of a diagonal of the base

LG = Lateral edge = a Cm

Full diagonal BG = √(a² + a²) = a√2 cm

Half diagonal

Applying Pythagoras theorem, we get:

LH = √(LG² – HG²)

Given: LH = 12cm

Thus

⇒ a = 12√2 cm

Volume of a pyramid

Volume of a pyramid