Slicing a Right Rectangular Prism with a Plane
Videos and solutions to help Grade 7 students learn how to describe rectangular regions that result from slicing a right rectangular prism by a plane perpendicular to one of the faces.
Plans and Worksheets for Grade 7
Plans and Worksheets for all Grades
Lessons for Grade 7
Common Core For Grade 7
New York State Common Core Math Grade 7, Module 6, Lesson 16
Lesson 16 Student Outcomes
• Students describe rectangular regions that result from slicing a right rectangular prism by a plane
perpendicular to one of the faces.
Lesson 16 Summary
• A slice, also known as a plane section, consists of all the points where the plane meets the figure.
• A slice made parallel to a face in a right rectangular prism will be parallel and identical to the face.
• A slice made perpendicular to a face in a right rectangular prism will be a rectangular region with a height
equal to the height of the prism.
Lesson 16 Classwork
Provide context to the concept of taking slices of a solid by discussing what comes to mind when we think of “taking a
slice” of something.
Consider a ball B. Figure 3 shows one possible slice of B.
a. What figure does the slicing plane form?
Students may choose their method
of representation of the slice (e.g.,
drawing a 2D sketch, a 3D sketch, or
describing the slice in words).
b. Will all slices that pass through be the
same size? Explain your reasoning.
c. How will the plane have to meet the ball so that the plane section consists of just one point?
The right rectangular prism in Figure 4 has been sliced with a plane
parallel to face ABCD. The resulting slice is a rectangular region
that is identical to the parallel face.
a. Label the vertices of the rectangular region defined by
the slice as WXYZ.
b. To which other face is the slice parallel and identical?
Discuss the following questions with your group.
1. The right rectangular prism in Figure 5 has been sliced with a
plane parallel to face LMON.
a. Label the vertices of the rectangle defined by the slice
b. What are the dimensions of the slice?
c. Based on what you know about right rectangular prisms, which faces must the slice be perpendicular to?
The right rectangular prism in Figure 6 has been sliced with a plane
perpendicular to BCEH. The resulting slice is a rectangular region
with a height equal to the height of the prism.
a. Label the vertices of the rectangle defined by the
slice as WXYZ.
b. To which other face is the slice perpendicular?
c. What is the length of ZY?
d. Joey looks at WXYZ and thinks that the slice may be a parallelogram that is not a rectangle. Based on what
is known about how the slice is made, can he be right? Justify your reasoning.
In the following exercises, the points at which a slicing plane meets the edges of the right rectangular prism have been
marked. Each slice is either parallel or perpendicular to a face of the prism. Use a straightedge to join the points to
outline the rectangular region defined by the slice and shade in the rectangular slice.
2. A slice parallel to a face.
3. A slice perpendicular to a face.
4. A slice perpendicular to a face.
In Exercises 5–6, the dimensions of the prisms have been provided. Use the dimensions to sketch the slice from each
prism and provide the dimensions of each slice.
5. A slice parallel to a face.
6. A slice perpendicular to a face.
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