GCSE›AQA GCSE Maths›Mind mapsMensuration and CalculationAQA GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover facts2D areasTriangle: 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21×base×heightParallelogram: base × perpendicular heightTrapezium: 12(a+b)h\frac{1}{2}(a+b)h21(a+b)haaa and bbb are the parallel sidesPerimeter = add all the outside lengthsCirclesCircumference: C=2πr=πdC = 2\pi r = \pi dC=2πr=πdArea: A=πr2A = \pi r^2A=πr2Composite shapes: split into simple partsIn terms of π\piπ means keep the symbolArcs and sectorsSector: slice between two radiiArc is the curved edgeArc length =θ360×2πr= \frac{\theta}{360} \times 2\pi r=360θ×2πrSector area =θ360×πr2= \frac{\theta}{360} \times \pi r^2=360θ×πr2Higher tier: frustum is a cone with the top cut offMensurationarea, volume and arcsπ\piπcm²cm³3D solidsPrism volume = cross-section area × lengthCylinders are prisms with a circular cross-sectionAlso needed: spheres, pyramids and conesComposite solids: add or subtract the partsWorked exampleSector: radius 6 cm, angle 90°Area =90360×π×62= \frac{90}{360} \times \pi \times 6^2=36090×π×62=14×36π= \frac{1}{4} \times 36\pi=41×36πAnswer: 9π9\pi9π cm²Exam tips'In terms of π\piπ': do not use a decimalMixing units (cm and m) is a common errorConvert units before calculatingCheck answer units: cm² for area, cm³ for volume