At the base of the pyramid lies a square with a side of 4 cm, side edges 6 cm. Find the height of the pyramid.

To find out the height of a given pyramid, we will use the Pythagorean theorem: h = √ (Lg ^ 2 – Lk ^ 2), where Lg is the length of the side edge (hypotenuse, Lg = 6 cm); Lk is the length of half of the diagonal of the square lying at the base (leg, Lk = 0.5d = 0.5 * a * √2, where a is the side of the base, square (a = 4 cm)).

Let’s perform the calculation: h = √ (Lg ^ 2 – Lk ^ 2) = √ (Lg ^ 2 – (0.5 * a * √2) ^ 2) = √ (6 ^ 2 – (0.5 * 4 * √ 2) ^ 2) = √ (36 – 8) = √28 = 2√7 cm.

Answer: The height of the given pyramid should be 2√7 cm.