Question

A cone is sliced so the cross section is perpendicular to its base and passes through its vertex.

Answer 1

The shape of the cross-section formed is a triangle, when a cone is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex.

Say, we have a cone as shown below. In the figure, the cone is sliced such that the cut passes the vertex of the cone and is perpendicular to the base of the cone (as shown by the dashed line). The figure thus formed after cutting is in the shape of a triangle.

Answer 2

A triangle because a true cone coming to a discrete point at the apex or vertex and with a plane slicing it perpendicular to the base and through the vertex would have to have the shape of a triangle by construction