SOLUTION: The pyramid ABCDE has a square base. The pyramid is 20cm high. Each sloping edge measures 30cm. Calculate the length of the side of the base.

Since all sloping edges have the same length and since the base of the pyramid is a square, the pyramid is a regular pyramid.

It means that the height of the pyramid falls into the center of the square at the base.

Connect the center of the square at the base with some vertex of the base,
and consider the right-angled triangle formed by the pyramid's height and this connection.

This right-angled triangle has the leg of 20 cm and the hypotenuse of 30 cm.
Hence, the other leg, which is our connection, is  =  = .

It means that the diagonal of the square at the base is .

Hence, the edge at the base has the measure of  =  = .

Answer. The length of the side of the base is .