Question

identify cross sections of solids
score: 1.75/5 penalty: 0.25 off
question
select the type of cross section formed when a right triangular prism is cut perpendicular to its base.
answer
square
rectangle
circle
pentagon
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Explanation:

Step1: Analyze the properties of a right - triangular prism and cross - section

A right - triangular prism has two triangular bases and three rectangular lateral faces. When we make a cut perpendicular to the base (which is a triangle), we are cutting through the lateral faces.

Step2: Determine the shape of the cross - section

Since the lateral faces of a right - triangular prism are rectangles and the cut is perpendicular to the base (so it is parallel to the lateral edges which are perpendicular to the base), the cross - section will have the same shape as the lateral face. A rectangle has four right angles and opposite sides equal. A square is a special case of a rectangle where all sides are equal. But we are not given any information that the prism has equal - length lateral edges and base side lengths. A circle is not possible as there are no curved surfaces in a right - triangular prism. A pentagon has five sides, and a right - triangular prism has only three lateral faces and two triangular bases, so a five - sided cross - section is not formed by a cut perpendicular to the base.

Answer:

rectangle