Generalising Surface area

What is the surface area of a cube of side length 1?
If we then cut this cube in half, and throw one of the halves away, what is surface area of the remaining cuboid?
Repeat the process, cut the shape in half along the same plane. What pattern can you see?

Screen Shot 2017-07-09 at 16.59.12

What is the general formula for the surface of a cuboid of width 1, depth 1 and height h?

What is the general formula for a cuboid of width 1, depth d and height h?

What is the general formula for a cuboid of width w, depth d and height h?

What other 3D shapes can you find the general formula for the surface area? Try:

  • A tetrahedron, side length a
  • A square based pyramid, base length a, height, h
  • A cylinder radius r, length l

 

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