All the edges of a regular quadrangular pyramid were increased 4 times. How many times will its surface area increase?

Since all faces of the pyramid are magnified 4 times, the pyramids are similar with a similarity factor of 4. The areas of similar figures are referred to as the square of the similarity factor.

Let the area of the original pyramid be S cm2.

Then the area of the new pyramid is K ^ 2 * S = 16 * S cm2.

Second way.

Let the lengths of all the raders of the pyramid be equal to X cm.

Then Sax = X ^ 2 cm2.

Sside = 4 * Srad = 4 * X ^ 2 * √3 / 4 = X ^ 2 * √3 cm2.

Then Sпов = X ^ 2 + X ^ 2 * √3 = X ^ 2 * (1 + √3) cm2.

Then, after increasing the ribs by 4 times:

Spov1 = (4 * X) ^ 2 * (1 + √3) = 16 * X ^ 2 * (1 + √3) cm2.

Answer: The area will increase 16 times.