Nets Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Nets.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A net is a two-dimensional layout of faces that folds into a three-dimensional solid.

Unfold a 3D solid like a cardboard box—the flat connected pattern you get is a net of that solid.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A net is a valid unfolding of a 3D solid—surface area is computed by summing the face areas in the net.

Common stuck point: Students choose face arrangements that cannot fold without overlap.

Sense of Study hint: Check edge matches and imagine folding one face at a time.

Worked Examples

Example 1

easy
Draw and describe the net of a rectangular prism (box) with dimensions 5 cm \times 3 cm \times 2 cm, and use the net to find the total surface area.

Solution

  1. 1
    Step 1: A rectangular prism has 6 faces arranged in 3 pairs of congruent rectangles: two 5 \times 3 faces (top/bottom), two 5 \times 2 faces (front/back), and two 3 \times 2 faces (left/right).
  2. 2
    Step 2: The net is obtained by unfolding: lay the bottom flat, unfold the four side faces out, and place the top opposite the bottom. It forms a cross or T-shape with 6 rectangles.
  3. 3
    Step 3: Calculate each pair's area: 2(5 \times 3) = 30 cm², 2(5 \times 2) = 20 cm², 2(3 \times 2) = 12 cm².
  4. 4
    Step 4: Total surface area = 30 + 20 + 12 = 62 cm².

Answer

Total surface area = 62 cm²
A net is the 2D unfolding of a 3D figure. For a rectangular prism, the net has 6 rectangles. Adding their areas (which is the total surface area) gives 62 cm². Nets make surface area calculation visually intuitive.

Example 2

medium
Describe the net of a regular triangular pyramid (tetrahedron with equilateral triangle faces) with edge length 6 cm. Find its total surface area using the net.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
How many faces does a triangular prism have, and what shapes are they? If the triangular base has base 4 cm and height 3 cm, and the prism length is 10 cm, find the surface area using a net.

Example 2

hard
A cylindrical can has radius 3 cm and height 10 cm. Describe its net and find the total surface area.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

surface areashapescross sections 3d