Question

A triangular pyramid is cut by a plane parallel to its base. The area of the triangle of intersection is only one-fourth of the base area. If the altitude of the pyramid is 30 cm, find the distance of the vertex of the pyramid to the cutting
plane.

Answer 1

Methinks it's 15 cm

Answer 2

If you scale the pyramid by a factor of 1/2 around the top vertex, the area will be scaled by a factor of (1/2)^2 = 1/4. Scale 30 cm by a factor of 1/2 and you get the result: 15 cm.