lesson
Use the fraction of a full turn
1 · Learn
A sector of central angle t degrees is t/360 of the full circle. Its arc length is that fraction of 2πr, and its area is that fraction of πr². These are different quantities with different units.
A sector's perimeter includes two radii as well as the arc. Do not report only the arc when asked for the whole boundary.
2 · Worked example
A 90° sector of radius 4 cm has arc 2π cm and area 4π cm². Its perimeter is 2π + 8 cm.
3 · Your turn
Find the area of a 60° sector with radius 6 cm.
Check your answer
(60/360) × 36π = 6π cm².
4 · Apply your learning
Draw the sector and label arc, radii and area before selecting a formula.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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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.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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