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MENSURATION LAB
Learn it by playing it
Four short missions on four live stages. Steer the dials, watch the ladder, the shapes and the circle react, and figure out the rules. When a mission glows green, read why it worked.
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Mission 1 of 4
Climb the unit ladder
One slider sets a length in millimetres on the ladder; the ladder restates it in centimetres and metres live. Set the marker to exactly 250 mm.
400 mm · = 40 cm · = 0.4 m
Before you touch the dial: 250 mm is how many centimetres?
Currently 400 mm - too long. Bring the marker back down.
Study notes
Units of measure C5.1 / E5.1
Length units scale by 10 each step: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
Area units scale by the square of the length factor: 1 cm² = 100 mm² and 1 m² = 10,000 cm², so converting cm² to m² divides by 10,000 - not by 100.
Volume units scale by the cube: 1 cm³ = 1000 mm³ and 1 m³ = 1,000,000 cm³.
Capacity links volume to liquid measure: 1 litre = 1000 cm³, so 1 m³ = 1000 litres; 1 ml = 1 cm³.
Mass runs 1000 g = 1 kg; convert before you calculate, never after mixing units in one formula.
Convert every measurement into one unit before substituting into a formula - a length in cm and a length in m in the same area calculation is the classic lost mark.
Area and perimeter C5.2 / E5.2
Perimeter is the distance around the edge - add every side, including any unlabelled ones you must deduce.
Rectangle: area = length x width. Parallelogram: area = base x perpendicular height - the slant side is a distractor.
Triangle: area = 1/2 x base x perpendicular height; any side can be the base as long as the height is measured at right angles to it.
Trapezium: area = 1/2 x (a + b) x h, where a and b are the two parallel sides and h is the perpendicular distance between them.
The syllabus gives only the triangle formula in the exam - the rectangle, parallelogram and trapezium formulas are expected knowledge.
Always check the height is perpendicular to the base; a slanted side length used as a height overestimates the area.
Circles, arcs and sectors C5.3 / E5.3
Circumference = pi x d = 2 x pi x r; area = pi x r². Both formulas are in the exam's List of formulas.
An arc is a fraction of the circumference: arc length = (angle / 360) x 2 x pi x r.
A sector is a fraction of the disc: sector area = (angle / 360) x pi x r².
Core questions use sector angles that are factors of 360 (60°, 90°, 120°, ...); Extended includes minor and major sectors with any angle - a major sector has angle over 180°.
If a question asks for an exact answer 'in terms of pi', leave pi symbolic: a semicircle of radius 6 cm has area 18pi cm².
A sector's perimeter includes the two radii as well as the arc - a common slip is to give the arc length only.
Surface area and volume C5.4 / E5.4
A prism is any solid with a uniform cross-section: volume = area of cross-section x length. That one idea covers cuboids, cylinders and triangular prisms alike.
Cuboid: volume = l x w x h; surface area = 2(lw + lh + wh) - count all six faces.
Cylinder: volume = pi x r² x h; curved surface area = 2 x pi x r x h (imagine unrolling the label into a rectangle of width 2 x pi x r).
Pyramid and cone: volume = 1/3 x base area x perpendicular height; a cone's curved surface area = pi x r x l, where l is the slant height, not the vertical height.
Sphere: volume = 4/3 x pi x r³; surface area = 4 x pi x r². All of these appear in the List of formulas.
Surface area questions often exclude a face (an open box, a cylinder without a lid) - sketch the solid and tick off the faces that actually exist.
Compound shapes and parts of shapes C5.5 / E5.5
Split a compound shape into rectangles, triangles and circles you know, then add the areas - or subtract the missing piece from a larger simple shape.
For an L-shape, either split it into two rectangles or complete the big rectangle and subtract the corner that is missing; check the answer both ways when you can.
Compound solids work the same way in 3D: volume of a capsule is the cylinder plus the two hemisphere ends, which together make one sphere.
Parts of solids scale the formula: half a sphere (a hemisphere) has volume 2/3 x pi x r³, and its total surface area adds the flat circular face, pi x r², to the curved 2 x pi x r².
Perimeters of compound shapes need care at the joins - internal edges where two pieces meet are not part of the outside boundary.
Estimating first (rounding each dimension) catches answers that are ten times too big, the most common mensuration error after unit slips.
EduTribe study notes - original material aligned to the Cambridge IGCSE Mathematics 0580 syllabus (2025-2027). Automated checks completed; not yet reviewed by an educator.