A learner works out the area of a plus-shaped tile made from five squares that each have sides of 4 centimetres. The learner writes: five squares of side 4 make a side of 20, so the area is 20 times 20, which is 400 square centimetres. Which statement names the mistake in this compound-area working and gives the correct area?
The working squares an edge that the five small squares never form; each square covers 16 square centimetres, so the tile covers 80 square centimetres.✓Bonne réponse
The working is sound, because five squares whose sides each measure 4 centimetres together enclose one large square whose side measures 20 centimetres.
The five side lengths should be added rather than squared, so the tile covers 20 square centimetres.
Only the four outer squares should be counted, so the tile covers 64 square centimetres.
Explication
Five squares arranged in a cross keep their own size, so the tile covers five lots of 4 times 4. Adding the side lengths first invents a 20 centimetre edge that no part of the tile actually has, and squaring that invented edge inflates the result five times over.