The idea in brief. Folding stacks paper. The flap is the same size as the place it came from. Looking down after one fold, the flap has left the old outline once and the paper underneath it is still paper. Unfolding adds that flap back once. In the lesson. A fold is one sheet, in two layers.
Lesson video, with the working
Folded paper
4 min 20 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
A rectangular strip of paper measures 26 cm by 8 cm. One end of the strip is folded over. The folded piece is 6 cm long. It lies flat on top of the rest of the strip. Find the area of the shape that can now be seen from above.
Area seen from above = 208 − 48 = 160 cm²
Ans: 160 cm²
Example 1
A rectangular strip of paper measures 30 cm by 9 cm. Both ends are folded inwards. Each fold is 7 cm. The two flaps lie flat on the strip. They do not meet. Find the area of the shape that can now be seen from above.
Area seen from above = 270 − 126 = 144 cm²
Ans: 144 cm²
Example 2
A sheet of paper ABCD measures 20 cm by 12 cm. Corner A lands on P. The crease XY has X on AB and Y on AD. The lengths AX and AY are equal. The shaded gap and flap have a total area of 64 cm². Find the length of AX.
AX = 8 cm
Ans: 8 cm
How to solve it
Watch the end fold over. What leaves the view is the flap, once. The dashed outline shows where it came from.
Write the rule: area seen from above is the area of the strip minus the flap.
Find the whole strip: 26 times 8 is 208 square centimetres.
Find the flap: 6 by 8 is 48 square centimetres.
Subtract: 208 minus 48 is 160 square centimetres. With two folds, take off both flaps.
The dashed triangle is where the flap came from. The shaded triangle is where it landed. They are the same piece of paper. A fold is one sheet, in two layers.
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
Question 1 of 10 · Basic · free to tryA rectangular sheet of paper is folded once so that one end lies flat on top…A rectangular sheet of paper is…
A rectangular sheet of paper is folded once so that one end lies flat on top of the rest. The shape that can be seen after folding measures 22 cm by 6 cm, and the flap lying on top of it measures 5 cm by 6 cm. Find the area of the sheet before it was folded.
How do you solve folded paper area questions in P6?
When paper is folded, one flap moves on top of the rest and the shape seen from above gets smaller.
What your child learns here
When paper is folded, one flap moves on top of the rest and the shape seen from above gets smaller. This Primary 6 page applies the outcome on area of composite figures to folded strips and sheets.
Find the area of the whole sheet before folding, using area of rectangle.
Find the area seen from above after a fold: the whole sheet minus one flap for each fold.
Recognise the part that is two layers thick, and count it once when it is asked for.
Work backwards from the folded shape: each fold gives its length back when the paper is opened.
Does the answer make sense?
The shape seen from above after a fold must have a smaller area than the flat sheet, because one flap now lies on top of the rest. The part two layers thick is smaller still, since it sits inside the shape your child can see from above.
How to practise these questions
Basic questions train what a fold changes and what it keeps, such as the breadth, and which part ends up two layers thick. Intermediate questions add two folds, or work backwards from the folded shape to the strip before folding. In the Challenge questions the flap must be counted twice, or a corner fold creates two identical triangles. If a folded paper question gets confusing, read the written step-by-step solution together.
Questions parents ask
Does folding change the area of the paper? No. The paper keeps its area, but part of it now lies on top of the rest, so the area seen from above is smaller.
What does the area seen from above mean? It is the area of the shape the folded paper makes on the table, with the two-layer part counted once.
Is folded paper area in the P6 syllabus? Folding is not named as a separate outcome. These questions apply the Primary 6 outcome on the area of composite figures made up of squares, rectangles and triangles to folded paper.
