11+ Area & Perimeter
Master 2D shape formulas, compound L-shape missing sides, multi-way shape splitting, and shaded border paths. Complete untimed, timed, and Year 4 exam-standard tests.
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Interactive Area & Perimeter Lab
Interactive Simulation · 4 ModulesExplore live unit grid counts, compound L-shape splitting engines, shaded border calculations, and speed challenge drills.
The 11+ Area & Perimeter Guide
Complete 2D shape formulas matrix, inverse dimension solvers, and critical examiner traps.
2D Shape Formulas & Inverse Rules
Commit these foundational formulas to memory. In 11+ exams, questions frequently require working backwards from area or perimeter to find missing side lengths.
| Shape | Perimeter Formula | Area Formula | Inverse Trick |
|---|---|---|---|
| Square | 4s | s² | s = P ÷ 4 or s = √Area |
| Rectangle | 2(l + w) | l × w | l = Area ÷ w |
| Triangle | a + b + c | ½ b × h | h = (2 × Area) ÷ b |
| Parallelogram | 2(a + b) | b × hperp | b = Area ÷ hperp |
| Trapezium | Sum of 4 sides | ½ (a + b) × h | Average of parallel sides × h |
Perimeter is distance around a fence (1D: mm, cm, m). Area is carpet covering a floor (2D: mm², cm², m²). Always verify units match before calculating (e.g. convert metres to cm if required).
3 Critical 11+ Geometry Traps
Many students mistakenly think cutting a corner out of a rectangle reduces its perimeter. It does NOT! The two cutout edges match the missing corner edges exactly.
In non-right triangles and parallelograms, examiners intentionally label the slanted side to trick students. For area, NEVER use the slant side; use the vertical perpendicular height!
When calculating the area of a path or frame surrounding a rectangle, you must subtract the border width twice (once for each side) to find the inner rectangle dimensions.
Inner L = Outer L - 2(Border) and Inner W = Outer W - 2(Border).Untimed area & perimeter test
5 questions · drawn from 25 · no timer · unlimited retakesWork through step-by-step 11+ Area and Perimeter problems at your own pace with detailed solution breakdowns.
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Timed area & perimeter test
5 questions · drawn from 25 · 4 minutes · unlimited retakesA 4-minute timed test to build speed, accuracy and confidence under exam conditions.
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Year 4 area & perimeter test
5 questions · drawn from 20 · no timer · unlimited retakesCore foundation test for Year 4 students covering simple rectangular perimeters and basic square counting.
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