Figure shows (a) an isosceles triangular prism and (b) a right circular cone whose diameter is the same length as the base of the triangle. The center of mass of the triangle is one- third of the way up from the base but that of the cone is only one-fourth of the way up. Can you explain the difference?

It can be seen from the figure below that the center of mass of prism is relatively closer to its base than the center of mass of triangular prism.

It is important to note that if the diameter of the circular cone is equal to the length of the triangular prism and the width of the triangular prism is smaller than its length, than the area of the base of right circular cone is larger than the area of the base of the isosceles triangular prism.
Therefore, more mass is concentrated toward the base of the cone relative to the base of triangular prism. This accounts for the fact that the center of mass of the right circular cone is near the base relative to the center of mass of isosceles triangular prism.