lesson
Boundary and surface need different measures
1 · Learn
Perimeter measures the outside boundary; area measures covered surface. A rectangle 8 cm by 5 cm has perimeter 26 cm and area 40 square cm.
For a rectilinear composite shape, split the surface into rectangles to find area and trace every outside edge for perimeter. Do not count interior splitting lines as boundary.
2 · Worked example
An 8 cm by 5 cm rectangle with a 3 cm by 2 cm top-right corner removed has area 40 − 6 = 34 square cm. Trace the remaining edges separately for perimeter.
3 · Your turn
Find the area and perimeter of a 9 cm by 4 cm rectangle. How could you estimate the area of an irregular drawn shape?
Check your answer
36 square cm; 26 cm. Overlay a square grid, count full squares and combine or estimate partial squares, stating that the result is approximate.
4 · Apply your learning
Draw a composite shape on squared paper, label lengths and calculate both measures using the appropriate units.
Adult guidance and safety
Model the calculation or measurement before relying on a procedure. Explain estimates, units and checks. Use a ruler/protractor and suitable diagrams where needed; text examples alone do not establish practical skill or fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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