Question

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

pentagon
parallelogram
triangle
hexagon

Explanation:

Identify the given points on the cuboid

The three given points are:

1. The bottom-front-left vertex.
2. A point on the top-front edge.
3. A point on the bottom-back edge.

Determine the intersecting plane

A plane passing through these three non-collinear points must intersect the faces of the cuboid:

• It cuts the front face along the segment connecting the bottom-left vertex to the point on the top-front edge.
• It cuts the top face starting from the point on the top-front edge.
• It cuts the back face containing the point on the bottom-back edge.
• It cuts the bottom face along the segment connecting the bottom-left vertex to the point on the bottom-back edge.

Count the intersecting edges

The plane intersects exactly four faces of the cuboid (front, top, back, and bottom), creating a 4-sided polygon (quadrilateral). Since opposite faces of a cuboid are parallel, the intersection lines on opposite faces are parallel, resulting in a parallelogram.

Answer:

• pentagon
• parallelogram (Correct answer)
• triangle
• hexagon