7.G.3: Describe Cross-Sections of 3D Figures
Also written as 7.G.A.3 and CCSS.MATH.CONTENT.7.G.A.3 · Cluster: Draw construct, and describe geometrical figures and describe the relationships between them.
The Official Wording
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Common Core State Standards, Grade 7, Geometry · Read it at the source · Checked October 14, 2026
What 7.G.3 Means in Plain English
Seventh graders picture slicing a solid and name the flat face the cut leaves. Slice a 10 by 6 by 4 cm block of clay parallel to its base and the cut face is a 10 by 6 cm rectangle; slice off one corner and it is a triangle.
Pyramids add shrinking slices: cut an 8 cm square pyramid parallel to its base halfway up and the slice is a 4 cm square. 8th grade moves on to cylinders, cones and spheres (8.G.9), and high school slices those solids too (HSG-GMD.4).
7.G.3 I Can Statements
- I can name the shape a slice through a box leaves.
- I can give the size of a slice parallel to a face.
- I can describe slices of a pyramid at different heights.
7.G.3 Worked Example
A block of clay and a square pyramid, each cut with a wire, and the flat face every cut leaves behind.
A clay block is a right rectangular prism 10 cm long, 6 cm wide and 4 cm tall. A square pyramid has a base 8 cm on each side and is 9 cm tall. Describe the slice when (a) the block is cut parallel to its base, (b) the block is cut parallel to its 6 by 4 end, (c) one corner of the block is sliced off, (d) the pyramid is cut parallel to its base halfway up, (e) the pyramid is cut straight down through its tip, parallel to a base edge.
- (a) and (b) A cut parallel to a face copies that face, wherever along the block it is made.(a) rectangle 10 cm by 6 cm; (b) rectangle 6 cm by 4 cm
- (c) The wire crosses only the three faces that meet at the corner, and each face it crosses gives the slice one edge.(c) triangle
- (d) A slice parallel to the base is a smaller copy of the base. Halfway up, the pyramid has narrowed to half its width.(d) square 4 cm by 4 cm
- (e) The cut runs across the base through its center, 8 cm wide, and rises to the tip, 9 cm up.(e) triangle with an 8 cm base and a 9 cm height
Check it: Count the faces the cut crosses: the slice has that many sides. The corner cut crosses 3 faces, so 3 sides; cut (a) crosses the 4 side faces of the block, so 4 sides. Slicing real clay with dental floss confirms each shape.
Common Mistakes with 7.G.3
Naming a solid instead of a flat shape
Cut parallel to the base, the slice is a smaller prism
Try this: Ask only for the cut face, the shape you could trace on paper: a slice is always flat, so name a polygon.
Keeping every pyramid slice full size
Halfway up the 8 cm pyramid, the slice is an 8 cm square
Try this: Measure the pyramid’s width at the height of the cut: halfway up it has narrowed to half, so the slice is a 4 cm square.
Expecting only rectangles from a box
Any cut through a rectangular prism makes a rectangle
Try this: Slice a corner off a real clay block and look: the cut crosses three faces, and three edges make a triangle.
Where 7.G.3 Fits
Practice 7.G.3
Quick Check
- A cereal box is 20 cm tall, 15 cm wide and 5 cm deep. What is the slice when it is cut parallel to its 15 by 5 cm top?
- A square pyramid has a 12 cm base. What is the slice parallel to the base, one third of the way down from the tip?
- What shape is the slice when a plane cuts a cube through only three of its faces near one corner?