The pattern
Rectangle and square measurement
Use opposite equal sides, undo the area or perimeter formula, and count each outside edge once.
A rectangle covered in square tiles gives two different numbers: how many squares sit inside it, and how far a pencil travels tracing its outer edge. The first is area, found by counting rows and columns of squares; the second is perimeter, found by adding the four sides. A composite shape made of several rectangles needs every outer edge traced in turn, including any sides not given directly.
How to spot it
Squares tiling a rectangle, or a shape made of several rectangles joined together, point here. The question asks for area, perimeter, or the length of a missing side.
Common mistake
Children multiply length by width when the question actually asks for perimeter. On a composite shape, they add only the labelled sides and miss the ones they must work out themselves.
25 worked solutions
Standard
- distinguish area from perimeter The shown 8-by-5 rectangle is covered with square tiles. Does the number of tiles describe its area or its perimeter?
- distinguish area from perimeter The shown 7-by-4 rectangle is covered with square tiles. Does the number of tiles describe its area or its perimeter?
- find a rectangle side from area A rectangle has area 63 cm² and length 9 cm. Find its width.
- find a rectangle side from area A rectangle has area 60 cm² and length 12 cm. Find its width.
- find a rectangle side from perimeter A rectangle has perimeter 32 cm and length 9 cm. Find its width.
- find a rectangle side from perimeter A rectangle has perimeter 28 cm and length 8 cm. Find its width.
- find a rectangle side from perimeter A rectangle has perimeter 34 cm and length 12 cm. Find its width.
- find a square side from area A square has area 81 cm². Find its side length.
- find a square side from area A square has area 64 cm². Find its side length.
- find a square side from perimeter A square has perimeter 36 cm. Find its side length.
- find a square side from perimeter A square has perimeter 32 cm. Find its side length.
- find rectangle area Find the area of the shown 9 cm by 4 cm rectangle.
- find rectangle area Find the area of the shown 8 cm by 5 cm rectangle.
- find rectangle perimeter Find the perimeter of the shown 9 cm by 4 cm rectangle.
- find rectangle perimeter Find the perimeter of the shown 8 cm by 5 cm rectangle.
- find rectilinear perimeter Find the perimeter of the shown rectilinear figure. Its outer width is 9 cm and outer height is 6 cm; the corner cut-out is 3 cm b…
- find rectilinear perimeter Find the perimeter of the shown rectilinear figure. Its outer width is 10 cm and outer height is 7 cm; the corner cut-out is 4 cm …
- find square area Find the area of the shown square with side 8 cm.
- find square area Find the area of the shown square with side 6 cm.
- find square perimeter Find the perimeter of the shown square with side 8 cm.
- find square perimeter Find the perimeter of the shown square with side 6 cm.
- measure area with square units How many square units cover the shown 7-by-3 rectangle?
- measure area with square units How many square units cover the shown 6-by-4 rectangle?
- perimeter of a composite rectilinear figure A composite rectilinear figure is formed by removing a 2 cm by 2 cm corner from a 9 cm by 6 cm rectangle. Find its perimeter.
- perimeter of a composite rectilinear figure A composite rectilinear figure is formed by removing a 4 cm by 3 cm corner from a 12 cm by 8 cm rectangle. Find its perimeter.
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.