Question

all the edges of the object in the diagram are equal in length. the object is cut by a vertical plane containing a and b and bisecting two of the horizontal edges. what is the shape of the cross - section resulting from the cut?
a. a regular hexagon
b. an equilateral triangle
c. a rhombus
d. a square

Explanation:

Step1: Analyze the object's edges

The object has all edges equal. The cut is a vertical plane through A, B, and bisecting two horizontal edges.

Step2: Determine cross - section sides

When we make the cut, the cross - section will have four sides. Since all edges of the original object are equal, the four sides of the cross - section will be equal in length. Also, the opposite sides will be parallel (due to the nature of the cut in a symmetric object with equal edges). A quadrilateral with four equal sides and opposite sides parallel is a rhombus. A regular hexagon has 6 sides, an equilateral triangle has 3 sides, and a square has four equal sides and right angles (but here the angles are not necessarily right angles as the cut is not at 90 degrees to the horizontal edges in a way that would form right angles, just equal - sided and parallel opposite sides).

Answer:

C. a rhombus