​Calculate the volume of a square pyramid if it has base area of 64 cm2, and the distance from the apex to a corner of the base is 15cm

Length of each side of base = \(+\sqrt{64}= 8\)

Using Pyth. Thm., Slant height = \(\sqrt{15^2-(\dfrac{8}{2})^2}=\sqrt{209}\)

Using Pyth. Thm. again, Height = \(\sqrt{(\sqrt{209})^2-(4)^2}=\sqrt{193}\)

Volume = \(\dfrac{1}{3}(8)^2(\sqrt{193})\)

=\(\dfrac{64\sqrt{193}}{3}\text{cm}^3\)