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Lesson · Grade 8 · Mathematics

Surface area: add the areas of every face

  • Grade 8
  • Mathematics
  • 2 min 7 s
  • British Columbia
  • BC8-MA-24

A closed box 10 cm by 6 cm by 4 cm unfolds into its net, and the faces are counted and coloured in three matching pairs: 2 × 60 + 2 × 40 + 2 × 24 = 248 cm², checked by adding all six faces one by one. It then shows two common mistakes, finding the volume (240 cm³) and counting only three faces (124 cm²), and ends on the recap "Surface area: add the areas of every face."

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In one sentence

The question this lesson answers

Here is a closed box. It is 10 centimetres long, 6 centimetres wide and 4 centimetres high. What is its surface area?

A box shape like this is called a rectangular prism. Each flat surface is called a face.

Transcript

What the lesson says

Here is a closed box. It is 10 centimetres long, 6 centimetres wide and 4 centimetres high. What is its surface area?

A box shape like this is called a rectangular prism. Each flat surface is called a face.

The surface area of a prism is the total area of all its faces.

Unfold the box into its net: the flat shape that folds up to make the box.

Count the faces: 1, 2, 3, 4, 5, 6.

Opposite faces are the same size, so the 6 faces make 3 matching pairs.

The top and the bottom are each 10 by 6. 10 times 6 is 60 square centimetres, and two make 120.

The front and the back are each 10 by 4. 10 times 4 is 40 square centimetres, and two make 80.

The two ends are each 6 by 4. 6 times 4 is 24 square centimetres, and two make 48.

Add the three pairs: 120 plus 80 plus 48 is 248 square centimetres.

Check by adding the six faces one by one: 60, 60, 40, 40, 24 and 24 also make 248.

A common mistake is to multiply 10 by 6 by 4. That gives 240 cubic centimetres: the volume, the space inside.

Another mistake is to add only three faces: 60 plus 40 plus 24 is 124, just half the surface.

Surface area: add the areas of every face. For this box, that is 248 square centimetres.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Geometry and measurement: surface area and volume of regular solids, including triangular and other right prisms and cylindersBC8-MA-24

Next: Surface Area of a Triangular Prism

The outcomes and strands follow the British Columbia curriculum.

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