Perimeter Question Generator
Builds a sheet of perimeter questions at the level you ask for, with the working and the answers hidden until you want them. Every figure is chosen so the perimeter comes out whole. Every question is computed and checked directly — not a fabricated or AI-guessed fact.
What this generator does
Generates perimeter questions with answers, across squares, rectangles, triangles, regular polygons and L-shapes. The L-shape at stretch level is where perimeter stops being a formula and becomes reasoning: cutting a corner out of a rectangle leaves the distance round it unchanged, which is not what most people expect.
How to use this tool
- Choose a level and how many questions you want.
- Press make questions and work through the sheet.
- Show the answers to mark it, or show the working to see which rule each question uses.
- Enter a seed word to rebuild the same sheet later.
Worked examples
- Rectangle, gentle level, seed round9
- A rectangle 9 cm wide and 4 cm tall → perimeter 26 cm, from one width and one height added and doubled.
Common use cases
- Perimeter practice at home or school
- Quick geometry warm-ups
- Self-testing before a maths quiz
How this generator works
Side lengths are drawn within the level's range for the chosen shape. A triangle's three sides are drawn subject to the triangle inequality — each side shorter than the sum of the other two — so the figure described could actually be drawn. An L-shape draws an outer rectangle and a smaller cut-out, and its perimeter is the outer rectangle's: the two cut edges replace exactly the lengths they removed, which is what the working explains.
Randomness and fairness
Dimensions are drawn with the browser's cryptographic random number generator and then constrained: a triangle's three sides must satisfy the triangle inequality, so no question describes a shape that cannot exist. Unless the generator has changed since, a seed word rebuilds the same sheet later; it is there for reproducibility, not cryptographic strength, and a seeded sheet is deterministic rather than unpredictable.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- There are no diagrams. The shape is described in words, which suits mental work and a printed sheet but is not the same as measuring a drawing.
- Circles are not included, because a circumference brings pi in and every answer here is a whole number a pupil can check. The circle geometry question generator sets circumference.
- An L-shape is described as a rectangle with a corner removed rather than drawn, so a pupil who cannot yet picture that will need it sketching first.
Common mistakes
- Confusing perimeter with area
- Perimeter is the distance around the edge and is measured in units. Area is the space inside and is measured in square units. The units are the giveaway.
- Missing a side on a compound shape
- Count the sides before adding. Compound shapes usually have more sides than the diagram labels.
Related generators
- Pythagoras Question GeneratorRight-triangle questions that use genuine Pythagorean triples for whole answers, or state the rounding when there is none.
- Area Question GeneratorArea questions built to order — rectangles, triangles, parallelograms, trapeziums and L-shapes — with worked steps and an answer key.
- Volume Question GeneratorVolume questions built to order — cubes, cuboids and prisms, including one with an L-shaped cross-section — with worked steps and an answer key.
- Circle Geometry Question GeneratorArea and circumference questions, sometimes from the diameter, with the halving step made explicit.