What you’ll learn
Describe 2D cross-sections of 3D figures.
Key idea
A parallel interior slice of a right rectangular prism has the corresponding face's rectangular outline.
A parallel interior slice retains that face's rectangular outline and two parallel dimensions; normal-axis length is not a section side.
Worked example
Enter the exact value or ordered values in the format requested below.
A right box has x,y,z side lengths 2,2,7cm. An interior slice is parallel to its xy face. Find its rectangular cross-section perimeter as a number of cm.
- The plane parallel to xy is perpendicular to the z direction; its section retains the x and y dimensions 2 and 2cm.
- This rectangle has perimeter2×(2+2)=8cm, not a triangular outline.
Answer: 8
Quick Check
Evaluate a worked attempt at describe 2d cross-sections of 3d figures, identify the first invalid step, and provide the correction.
Right box dimensions x,y,z=2,3,8cm, interior slice parallel to xz. Step1 identifies the corresponding face as rectangular. Step2 calls the cross-section a triangle. Locate the first invalid step and correct shape and dimensions.