Three-Dimensional Figures - Seventh Grade
Bases, Nets, Views & Cross Sections
1. Understanding Three-Dimensional Figures
What is a 3D Figure?
A 3D figure is a solid shape that has
THREE dimensions:
• Length (how long)
• Width (how wide)
• Height (how tall)
Also called SOLID FIGURES
Types of 3D Figures
Polyhedrons: Made of flat polygonal faces
Examples: Prisms, Pyramids, Cubes
Non-Polyhedrons: Have curved surfaces
Examples: Spheres, Cylinders, Cones
2. Bases of Three-Dimensional Figures
What is a Base?
The base is the face upon which
the 3D figure "sits" or rests
Some figures have 1 base, some have 2
Prisms
Prisms have TWO parallel congruent bases
Named by the shape of their base:
• Triangular Prism: 2 triangle bases
• Rectangular Prism: 2 rectangle bases
• Pentagonal Prism: 2 pentagon bases
• Hexagonal Prism: 2 hexagon bases
• Cube: 2 square bases (all faces are squares)
Pyramids
Pyramids have ONE base
Named by the shape of their base:
• Triangular Pyramid: 1 triangle base (also called tetrahedron)
• Square Pyramid: 1 square base
• Pentagonal Pyramid: 1 pentagon base
• Hexagonal Pyramid: 1 hexagon base
Other 3D Figures
Cylinder: 2 circular bases (parallel and congruent)
Cone: 1 circular base
Sphere: NO base (all points equidistant from center)
3. Nets of Three-Dimensional Figures
What is a Net?
A net is a 2D pattern that can be FOLDED
to make a 3D figure
It shows all the faces of the solid laid out flat
Common Nets
Cube Net
• 6 square faces
• All squares are equal in size
• Multiple net patterns possible
Rectangular Prism (Cuboid) Net
• 6 rectangular faces
• Opposite faces are congruent
Triangular Prism Net
• 2 triangular bases
• 3 rectangular faces
• Total: 5 faces
Square Pyramid Net
• 1 square base
• 4 triangular faces
• Total: 5 faces
Cylinder Net
• 2 circles (top and bottom)
• 1 rectangle (curved surface when flat)
Cone Net
• 1 circle (base)
• 1 sector (curved surface)
Key Points About Nets
✓ One 3D figure can have MULTIPLE different nets
✓ When folded, edges must meet perfectly
✓ Nets help calculate SURFACE AREA
✓ Count the faces to identify the shape
4. Front, Side, and Top Views
Understanding Different Views
Different views show what a 3D figure looks like
from different perspectives
Each view is a 2D representation
The Three Main Views
Front View
• What you see looking at the FRONT of the figure
• Shows height and width
Side View
• What you see from the SIDE (left or right)
• Shows height and depth
Top View
• What you see looking DOWN from above
• Shows length and width
Examples
Rectangular Prism (Box)
• Front View: Rectangle
• Side View: Rectangle
• Top View: Rectangle
Cylinder
• Front View: Rectangle
• Side View: Rectangle
• Top View: Circle
Square Pyramid
• Front View: Triangle
• Side View: Triangle
• Top View: Square
Cone
• Front View: Triangle
• Side View: Triangle
• Top View: Circle
Sphere
• Front View: Circle
• Side View: Circle
• Top View: Circle
5. Cross Sections of Three-Dimensional Figures
What is a Cross Section?
A cross section is the 2D shape you get
when you SLICE through a 3D figure with a plane
Think of cutting through an object with a knife!
Types of Cross Sections
Parallel to the Base:
The cross section has the SAME SHAPE as the base
Perpendicular to the Base:
The cross section is at a 90° angle to the base
Diagonal (at an angle):
The cross section can create different shapes
Cross Sections by Shape
Rectangular Prism (Cuboid)
Parallel to base: Rectangle (same as base)
Perpendicular: Rectangle
Diagonal: Rectangle or parallelogram
Cube
Parallel to base: Square
Perpendicular: Square or rectangle
Diagonal: Rectangle, triangle, trapezoid, or hexagon
Cylinder
Parallel to base: Circle (same as base)
Perpendicular: Rectangle
Diagonal: Oval (ellipse)
Cone
Parallel to base: Circle (smaller as you go up)
Through vertex: Triangle
Diagonal: Hyperbola or parabola
Square Pyramid
Parallel to base: Square (smaller as you go up)
Through vertex: Triangle
Perpendicular: Triangle or trapezoid
Sphere
Any direction: Always a CIRCLE
The circle gets larger toward the center
Triangular Prism
Parallel to base: Triangle (same as base)
Perpendicular: Rectangle
Key Concept
When you slice PARALLEL to the base,
the cross section is the SAME SHAPE
as the base!
Quick Reference: 3D Figures Summary
| 3D Figure | Number of Bases | Shape of Base(s) |
|---|---|---|
| Rectangular Prism | 2 | Rectangles |
| Triangular Prism | 2 | Triangles |
| Cube | 2 | Squares |
| Cylinder | 2 | Circles |
| Square Pyramid | 1 | Square |
| Cone | 1 | Circle |
| Sphere | 0 | No base |
💡 Important Tips to Remember
✓ Prisms: Have 2 parallel congruent bases
✓ Pyramids: Have 1 base and triangular faces
✓ Nets: 2D patterns that fold into 3D shapes
✓ Multiple nets: One shape can have different net patterns
✓ Views: Front, side, and top show different perspectives
✓ Cross section: 2D shape from slicing 3D figure
✓ Parallel slice: Cross section = same shape as base
✓ Sphere: Any cross section is always a circle
✓ Cylinder parallel: Cross section is a circle
✓ Cylinder perpendicular: Cross section is a rectangle
🧠 Memory Tricks & Strategies
Prism vs Pyramid:
"Prism has two bases like a pair, Pyramid points up with just one to spare!"
Nets:
"A net lays flat on the floor, fold it up to see 3D once more!"
Cross Sections Parallel to Base:
"Slice it parallel, you'll see - same shape as the base guaranteed!"
Sphere Cross Section:
"Slice a sphere any way you choose - a circle is what you'll never lose!"
Views:
"Front, side, and top make three - different views for all to see!"
Cylinder:
"Cylinder has circles on top and base, rectangles on the curved surface place!"
Master Three-Dimensional Figures! 📦 🔺 ⚽
Remember: Slice parallel to base = same shape as base!