MathBrush
←  All problems

P3 Rectangle and square measurement

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 by 2 cm.

A rectilinear figure with outer width 9 cm and outer height 6 cm; a corner is cut away.9 cm6 cm3 cm2 cm
One step of the worked solution to find rectilinear perimeter, drawn in pencil.
5 steps, drawn in pencil

See all 5 steps

MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.

I have a code → See a free one like it

65 worked examples are free without a code, two from every pattern. No account, either way.

The pattern behind it: Rectangle and square measurement

Use opposite equal sides, undo the area or perimeter formula, and count each outside edge once.

In this one. For this corner cut-out, the two new edges replace equal parts of the outer rectangle, so the perimeter is unchanged.

Undo or tracearea48 split into rows of 8 gives width 6perimeterfour equal square sides

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.

Try one like it

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?
All 14 with this pattern →

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.