Worksheet 3 Framed tiles

A quicker way of working out

Working with square shaped areas

Hassan notices that the apprentice finds it difficult to work out how many tiles are needed to fill an area, and the length of ribbon needed. Hassan knows that this can be worked out easily for any size shape. He uses square tiles and formulae to get the answers.

What is the formula for each of the following situations?

• The number of tiles needed to fill a square area

• The length of the border ribbon to surround a square area

Working with a different shape area

Hassan also tiles rectangles. Usually in his work the longer side is twice as long as the shorter side. What will the formulae be now for the number of tiles and for the length of the border ribbon?

A general case

Hassan uses tiles that are 1 cm x 1 cm. What is the formula to calculate:

• the number of tiles?

• the border ribbon length?