lesson
Use definitions, not orientation
1 · Learn
A regular polygon has equal sides and equal angles. A rhombus has equal sides, but if its angles are not all equal it is not regular. A square is a regular quadrilateral.
A cuboid in a flat drawing represents a solid with depth. Some edges may be hidden. Turning the picture does not change the solid's properties or the number of faces.
A rectangle has four right angles, even when it is tilted. If three corners are labelled 90 degrees and the fourth is unlabelled, its angle is also 90 degrees. Side length does not change this property.
2 · Worked example
A rectangle with perimeter 30 cm and length 9 cm has widths totalling 12 cm, so each width is 6 cm. I use the equal opposite sides.
3 · Your turn
Is every equal-sided quadrilateral regular? A rectangle has length 8 cm and perimeter 28 cm; find its width.
Check your answer
No: the angles must also be equal. The rectangle's width is 6 cm.
4 · Apply your learning
Compare solid models with drawings and identify hidden faces. Sort measured polygons by the stated definitions.
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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