Today’s problem — free all day, every step. Every day has one.
Eleven planks — the area of PQRS
11 identical wooden planks are nailed together to build a large rectangular fence panel PQRS. 3 planks lie flat along the top and 8 planks stand upright below them, as shown. The perimeter of PQRS is 210 cm. Find the area of PQRS.
Show the answerHide the answer
Each plank is 24 cm by 9 cm. PQ = 72 cm, PS = 33 cm, so the area of PQRS is 2376 cm².
The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. Repeated identity — one edge measured two ways gives one equation. PQ is 3 plank lengths and the very same PQ is 8 plank breadths, so 3L = 8B, and that alone fixes the shape of a plank.
How to spot it
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Common mistake
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Try one like it
Standard Water — poured into a second container A rectangular tank measures 30 cm by 20 cm by 25 cm. It is 3/5 full of water. All the water is poured into a second rectangular co…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.