Revision notes, worked examples and methods for perimeter, area and circles.
Notes and quizzes ready · 50 questions · Revision video ready.
Foundation shows shared notes and questions. Higher includes the shared content and labelled Higher extensions. Changing tier starts the notes and a new quiz set.
Revise the key ideas
Perimeter and area
Perimeter is the total boundary length; area measures the enclosed surface. Perimeter uses units such as cm; area uses cm2. Add only actual outside edges for a composite shape.
A rectangle has area lw. A triangle has area 12bh, where h is perpendicular to the base, even if its foot lies outside the triangle. A triangle with perpendicular height
A parallelogram has area bh, using perpendicular height rather than sloping side. A trapezium has area 12(a + b)h, where a and b are its parallel sides.
Worked example: A trapezium with parallel sides 5 cm and 9 cm and height 4 cm has area 12 × (5 + 9) × 4 = 28 cm2.
For a composite area, split into familiar shapes or subtract a missing region from a larger one. Label dimensions and check that pieces neither overlap nor leave gaps.
Circles and their parts
A radius joins centre to circumference; a diameter passes through the centre and is twice the radius. A chord joins two circumference points; a tangent touches at one point. An arc is part of the circumference. Radius, diameter, chord and tangent
A sector is enclosed by two radii and an arc. A segment is enclosed by a chord and an arc. They are different regions.
Circumference C = 2πr = πd; area A = πr2. Use the radius in the area formula, not the diameter.
Worked example: For radius 4 cm, circumference is 8π cm ≈ 25.13 cm and area is 16π cm2 ≈ 50.27 cm2. Keep π when an exact answer is required.
A semicircle's perimeter includes its diameter: πr + 2r. Its curved edge alone has length πr. For r = 3 cm, perimeter is 3π + 6 cm.
Arcs and sectors
For angle θ in degrees, arc length = θ360 × 2πr and sector area = θ360 × πr2. These use the fraction of a full turn. A sixty-degree sector of radius six
Worked example: A 60° sector of radius 6 cm has arc length 2π cm and area 6π cm2. Its perimeter is 12 + 2π cm, including both radii.
To find θ from a sector area, rearrange θ = 360 × sector areaπr2. Check whether the question describes a minor or major sector.
Convert lengths before calculating area. Doubling a length unit conversion without squaring it gives an incorrect area conversion.
Test yourself
50 questions · Sets of 10 from the selected tier. For fractions, use / when typing; for powers, use superscripts or ^. Follow each question's answer format. These quick checks support revision; practise full written solutions and proofs too.
Watch M30 · Perimeter, area and circles
Revise perimeter, area and circles with this narrated video. Use the player controls to pause, seek, adjust the volume or mute. Turn English captions on or off using the captions menu.
Mr Kidman's Classroom
