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Grade 6 · Maths · Lessons
Unfold the box
📦box🧩net🔺pyramid📐surface area
Unfold the box.
The big ideaA net is a solid unfolded flat. Add the areas of its faces to get the surface area.

How it works

A net is a solid unfolded flat. Add the areas of its faces to get the surface area.

A box has 6 faces in 3 matching pairs.

A square pyramid has a square base and 4 triangle faces.

Pairs of faces• 6 × 5 = 30 (two)• 6 × 4 = 24 (two)• 5 × 4 = 20 (two)Surface area• 2 × (30 + 24 + 20)• = 148
A 6 by 5 by 4 box.

Example 1: A box

  1. A box is 6 ft by 5 ft by 4 ft.
  2. Faces: 30, 24 and 20, each twice. 30 + 24 + 20 = 74.
  3. Double: 74 × 2 = 148 square feet.

Example 2: Count equal faces

  1. In a triangular prism, count which faces are 6 by 7.
  2. Look for matching faces on the net.
  3. Matching faces have the same area.

Example 3: A pyramid

  1. A square pyramid has a 4 m by 4 m base and 4 triangle faces.
  2. Base: 4 × 4 = 16. Each triangle of base 4 and height 4: 4 × 4 ÷ 2 = 8, and 4 of them make 32.
  3. 16 + 32 = 48 square meters.

Words to know

net
A flat pattern that folds into a solid.
surface area
The total area of all the faces.

Watch out

Try it

  1. A cube has edges of 3. What is one face's area?
  2. How many faces does a cube have?
  3. A cube has edges of 3. What is its surface area?
  4. What is a net?
Answers: 1. 9 · 2. 6 · 3. 54 · 4. a solid unfolded flat
For grown-upsUnfold a cereal box and find the area of each face.
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