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Identify cross-sections of 3D objects and solids generated by rotating 2D objects.

Identify the cross-section formed when a prism is sliced parallel to its base

Problem
If a rectangular prism is cut parallel to its base, what cross-section is formed?
Neutral method card that does not show the requested cross-section. Open full size
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Hint

Identify the shape of the prism's base before naming the cross-section.

A plane parallel to a prism's base creates a cross-section congruent to that base.

Solution walkthrough

01

Identify the slicing orientation

\[\text{cutting}~\text{plane}~\text{is}~\text{parallel}~\text{to}~\text{the}~\text{rectangular}~\text{base}\]

A parallel plane has the same orientation as the prism's base and stays at a constant height through the prism.

02

Track the intersection boundary

\[\text{each}~\text{cross}-\text{section}~\text{edge}~\text{corresponds}~\text{to}~\text{one}~\text{base}~\text{edge}\]

In a right prism, parallel vertical edges carry the base boundary unchanged to every height.

03

Compare dimensions

\[\text{section}~\text{side}~\text{lengths}~\text{equal}~\text{the}~\text{base}~\text{side}~\text{lengths}\]

A plane parallel to the base does not tilt or scale the rectangle, so the cross-section and base are congruent.

04

Name the cross-section

\[\text{rectangle}~\cong~\text{the}~\text{base}\]

The parallel cut produces the same rectangular shape and dimensions as the prism's base.

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Another way

  1. Imagine sliding the rectangular base upward through the prism; every intermediate position traces the same congruent rectangle.

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Common mistake

Do not call the section merely a rectangle and omit congruence. A parallel cut through a rectangular prism preserves the base dimensions.

Answer diagram for M3-037-A01-V01: the same slice with the exact cross-section name and extracted polygon.

Solution walkthrough video