GCSE›Edexcel GCSE Maths›Mind mapsPerimeter, Area and VolumeEdexcel GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover facts2D shapesTriangle: ½ × base × heightParallelogram: base × perpendicular heightTrapezium: 12(a+b)h\frac{1}{2}(a+b)h21(a+b)hComposite: split into simple shapes, then add or subtractTrapezium 5, 9, h = 4 gives 28 cm²CirclesCircumference =2πr=πd= 2\pi r = \pi d=2πr=πdArea =πr2= \pi r^2=πr2Arc length =θ360×2πr= \frac{\theta}{360} \times 2\pi r=360θ×2πrSector area =θ360×πr2= \frac{\theta}{360} \times \pi r^2=360θ×πr2Radius 6, angle 120°: arc 4π cmPrisms and cylindersPrism volume: base area × lengthCylinder volume =πr2h= \pi r^2 h=πr2hCurved surface area =2πrh= 2\pi r h=2πrhTotal surface area =2πrh+2πr2= 2\pi r h + 2\pi r^2=2πrh+2πr2Area and volumeperimeter, area, volumeπr2\pi r^2πr22πr2\pi r2πrCones, pyramids, spheresPyramid volume: 13×\frac{1}{3} \times31× base area × heightCone volume =13πr2h= \frac{1}{3}\pi r^2 h=31πr2hCone curved area =πrl= \pi r l=πrl, with slant height lSphere volume =43πr3= \frac{4}{3}\pi r^3=34πr3Sphere surface area =4πr2= 4\pi r^2=4πr2Composite solidsWork out each solid separatelyAdd volumes togetherHidden faces where solids join are not countedCylinder r=2, h=5 plus hemisphere: 763π\frac{76}{3}\pi376π cm³Exam tipsLeave answers in terms of π unless told otherwiseUse radius, not diameter, in areaSlant height for curved area, vertical height for volumePerpendicular height is at 90° to the base