The base of a right pyramid is a square of side 12\(\sqrt {2}\) cm and each of its slant edge is of length 15 cm.  What is the volume of the pyramid?

864 cm²

AM = 15 cm

Diagonal of square ABCD = \(\sqrt {2}\)a = \(\sqrt {2}\) × 12\(\sqrt {2}\) = 24 cm

Half of diagonal = OA = \(\frac{24}{2}\) = 12 cm

Therefore, height = 9  (9, 12, 15 ← Triplets)

Vol. of pyramid = \(\frac{1}{3}\) × base area × h

= \(\frac{1}{3}\) × 12\(\sqrt {2}\) × 12\(\sqrt {2}\) × 9 = 864 cm²