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Welcome to GCSE Edexcel Maths revision.

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Topic M 30: Perimeter, area and circles.

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This video covers Foundation and Higher tiers.

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Perimeter is the total boundary length; area measures the enclosed surface.

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Perimeter uses units such as cm; area uses square centimetres .

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Add only actual outside edges for a composite shape.

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A rectangle has area l w.

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A triangle has area 1 over 2 bh, where h is perpendicular to the base, even if its foot lies outside the triangle.

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A triangle with perpendicular height

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A parallelogram has area bh, using perpendicular height rather than sloping side.

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A trapezium has area 1 over 2 multiplied by open bracket a plus b close bracket h, where a and b are its parallel sides.

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Worked example: A trapezium with parallel sides 5 centimetres and 9 centimetres and height 4 centimetres has area 1 over 2 multiplied by open bracket 5 plus 9 close bracket multiplied by 4 equals 28 square centimetres .

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For a composite area, split into familiar shapes or subtract a missing region from a larger one.

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Label dimensions and check that pieces neither overlap nor leave gaps.

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A radius joins centre to circumference; a diameter passes through the centre and is twice the radius.

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A chord joins two circumference points; a tangent touches at one point.

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An arc is part of the circumference.

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Radius, diameter, chord and tangent

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A sector is enclosed by two radii and an arc.

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A segment is enclosed by a chord and an arc.

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They are different regions.

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Circumference C equals 2 pi r equals pi d; area A equals pi r squared .

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Use the radius in the area formula, not the diameter.

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Worked example: For radius 4 centimetres,

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circumference is 8 pi cm is approximately equal to 25.13 centimetres and area is 16 pi square centimetres is approximately equal to 50.27 square centimetres .

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Keep pi when an exact answer is required.

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A semicircle's perimeter includes its diameter: pi r plus 2 r.

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Its curved edge alone has length pi r.

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For r equals 3 centimetres, perimeter is 3 pi plus 6 centimetres.

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For angle theta in degrees,

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arc length equals the fraction with numerator open bracket theta close bracket and denominator open bracket 360 close bracket ,

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end fraction multiplied by 2 pi r and sector area equals the fraction with numerator open bracket theta close bracket and denominator open bracket 360 close bracket ,

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end fraction multiplied by pi r squared .

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These use the fraction of a full turn.

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A sixty-degree sector of radius six

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Worked example: A 60 degrees sector of radius 6 centimetres has arc length 2 pi cm and area 6 pi square centimetres .

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Its perimeter is 12 plus 2 pi cm, including both radii.

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To find theta from a sector area,

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rearrange theta equals the fraction with numerator open bracket 360 multiplied by sector area close bracket and denominator open bracket pi r squared close bracket ,

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end fraction .

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Check whether the question describes a minor or major sector.

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Convert lengths before calculating area.

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Doubling a length unit conversion without squaring it gives an incorrect area conversion.

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That completes Perimeter, area and circles.

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Revisit the notes and test yourself on the revision website.