Question

which shape will result from taking a cross section of the tetrahedron through the points shown?

triangle
square
trapezoid
pentagon

Explanation:

Identify the given points on the tetrahedron

The image shows a tetrahedron with three red points marked:

• One point is at the top vertex.
• One point is on the bottom-left edge.
• One point is on the bottom-right edge.

Determine the intersecting plane

A plane passing through three non-collinear points on a 3D solid defines a unique cross-sectional slice. Since there are exactly three distinct points on the boundary of the tetrahedron, the intersecting plane passes through these three points.

Determine the resulting cross-sectional shape

The intersection of a plane with a 3D solid forms a polygon whose vertices are the points where the plane intersects the edges of the solid. Since the plane passes through exactly three points on the edges/vertices of the tetrahedron, the resulting cross section is a polygon with 3 vertices, which is a triangle.

Answer:

• triangle (Correct answer)
• square
• trapezoid
• pentagon