Surface area from a net, step by step

A net is a box laid flat, and every one of its faces is out in the open where a child can point at it.

The question
5135 cm²

Surface area of a 5 × 5 × 13 box

5 × 5 × 13 cm
front and back:2 × 5 × 13 =130
front and back:2 × 5 × 13 =130
the two sides:2 × 5 × 13 =130
front and back:2 × 5 × 13 =130
the two sides:2 × 5 × 13 =130
top and bottom:2 × 5 × 5 =50
front and back:2 × 5 × 13 =130
the two sides:2 × 5 × 13 =130
top and bottom:2 × 5 × 5 =50
total:310
  1. A net lays all six faces out flat, so none of them is hidden — which is the whole reason a net is easier than the solid. They still come in three PAIRS.
  2. Front and back are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.
  3. The two sides are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.
  4. Top and bottom are 5 by 5, and they are identical — so that pair is 2 × 5 × 5 = 50.
  5. Three pairs, six faces, none missed: 130 + 130 + 50 = 310 square cm.

How it works.

  1. 01

    A net lays all six faces out flat, so none of them is hidden — which is the whole reason a net is easier than the solid. They still come in three PAIRS.

  2. 02

    Front and back are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.

  3. 03

    The two sides are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.

  4. 04

    Top and bottom are 5 by 5, and they are identical — so that pair is 2 × 5 × 5 = 50.

  5. 05

    Three pairs, six faces, none missed: 130 + 130 + 50 = 310 square cm.