Surface Area & Nets • Topic 1 of 2

Nets of 3D Shapes

What is a Net?

A net is a 2-dimensional diagram that can be folded to form a 3-dimensional shape. Think of it as the "pattern" or "unfolded" version of a solid.

Common Nets:

3D ShapeNet Description
Rectangular Prism6 rectangles (2 pairs of equal faces)
Cube6 identical squares
Triangular Prism2 triangles + 3 rectangles
Square Pyramid1 square + 4 triangles
Triangular Pyramid (Tetrahedron)4 triangles

Drawing Nets Tips:

  • Identify all faces of the 3D shape
  • Arrange faces so they connect along edges
  • Make sure net can fold without overlap
NET OF A RECTANGULAR PRISM:

 Front: 3×5 Top: 4×5
 Back: 3×5 Bottom: 4×5
 Left: 3×4 Right: 3×4
 
 One possible net arrangement:
 
 ┌─────────┐
 │ Top │
 │ 4 × 5 │
 ┌─────────┬─────┼─────────┼─────┬─────────┐
 │ Left │Front│ Bottom │Back │ Right │
 │ 3 × 4 │3×5 │ 4 × 5 │3×5 │ 3 × 4 │
 └─────────┴─────┴─────────┴─────┴─────────┘


NET OF A CUBE (6 identical squares):

 Two possible nets:
 
 ┌───┐
 │ │
 ┌───┼───┼───┐
 │ │ │ │
 └───┼───┼───┘
 │ │
 └───┘
 
 ┌───┐
 ┌───┼───┼───┐
 │ │ │ │
 └───┼───┼───┘
 │ │
 └───┘


NET OF A TRIANGULAR PRISM:

 Two triangles + three rectangles
 
 ┌─────┐
 │ / │
 │/ │
 └─────┘
 ┌─────┬─────┬─────┐
 │ │ │ │
 │Rect1│Rect2│Rect3│
 │ │ │ │
 └─────┴─────┴─────┘
 ┌─────┐
 │ / │
 │ V │
 └─────┘


NET OF A SQUARE PYRAMID:

 One square base + four triangles
 
 /
 / 
 / 
 /______
 / /
 / / 
 / / 
 /______/______
 ┌─────────────┐
 │ │
 │ Square │
 │ Base │
 └─────────────┘
Solved Examples
1
Worked Example

How many faces does a net of a rectangular prism have? What shapes are they?

Solution
  • Rectangular prism has 6 faces
  • All faces are rectangles (could include squares)
  • Answer: 6 rectangles
2
Worked Example

Draw a net for a cube with side length 2 cm.

Solution
  • Draw 6 squares, each 2×2, arranged in a cross shape
  • Fold lines between squares
  • Answer: Net shown in diagram
3
Worked Example

A triangular prism has triangle bases with base 4 cm and height 3 cm. The rectangular faces are 4×5, 5×5, and 5×5? Wait, need dimensions: triangular base sides 4,5,5 cm, prism height 5 cm. Identify all faces.

Solution
  • 2 triangles (base 4, height 3) → area each = 6 cm²
  • 3 rectangles: 4×5=20, 5×5=25, 5×5=25
  • Total 5 faces

Key Points

  • Net = unfolded 3D shape
  • All faces are connected along edges
  • Net must fold without gaps or overlaps
  • Different nets possible for same 3D shape
  • Practice visualizing folding
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A net is a 2D pattern that folds into a:
Explanation: A solid.
Q2.A cube's net has how many square faces?
Explanation: Six.
Q3.A cuboid has how many faces?
Explanation: Six.
Q4.A cylinder's net has $2$ circles and $1$:
Explanation: A rectangle.
Practice more MCQs → 📝 Assignment · 35 marks