What are the mensuration formulas in maths? How can we remember mensuration formulas?

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What is Mensuration?Mensuration is the branch of mathematics that deals with the measurement of geometric figures and their parameters like length, area, volume, and surface area. It's essential for solving real-world problems involving space and measurements.2D Mensuration Formulas (Area and Perimeter)Basic ShapesShapeArea FormulaPerimeter FormulaKey VariablesRectangleA = l × bP = 2(l + b)l = length, b = breadthSquareA = a²P = 4aa = side lengthTriangleA = ½ × b × hP = a + b + cb = base, h = height, a,b,c = sidesRight TriangleA = ½ × base × heightP = a + b + cUse Pythagoras: c² = a² + b²Equilateral TriangleA = (√3/4) × a²P = 3aa = side lengthParallelogramA = b × hP = 2(a + b)b = base, h = height, a,b = sidesRhombusA = ½ × d₁ × d₂P = 4ad₁, d₂ = diagonals, a = sideTrapeziumA = ½ × (a + b) × hP = a + b + c + da,b = parallel sides, h = heightAdvanced 2D ShapesShapeArea FormulaPerimeter/CircumferenceKey VariablesCircleA = πr²C = 2πrr = radiusSemicircleA = πr²/2P = πr + 2rr = radiusSectorA = (θ/360°) × πr²Arc length = (θ/360°) × 2πrθ = angle in degreesRing/AnnulusA = π(R² - r²)-R = outer radius, r = inner radiusEllipseA = πabP ≈ π[3(a+b) - √((3a+b)(a+3b))]a,b = semi-major and semi-minor axes3D Mensuration Formulas (Volume and Surface Area)Basic 3D ShapesShapeVolume FormulaTotal Surface AreaCurved Surface AreaKey VariablesCubeV = a³TSA = 6a²-a = side lengthCuboidV = l × b × hTSA = 2(lb + bh + hl)-l = length, b = breadth, h = heightCylinderV = πr²hTSA = 2πr(r + h)CSA = 2πrhr = radius, h = heightConeV = ⅓πr²hTSA = πr(r + l)CSA = πrlr = radius, h = height, l = slant heightSphereV = (4/3)πr³TSA = 4πr²Same as TSAr = radiusHemisphereV = (2/3)πr³TSA = 3πr²CSA = 2πr²r = radiusAdvanced 3D ShapesShapeVolume FormulaTotal Surface AreaKey VariablesFrustum of ConeV = (π/3)h(r₁² + r₁r₂ + r₂²)TSA = π(r₁ + r₂)l + π(r₁² + r₂²)r₁,r₂ = radii, h = height, l = slant heightPyramidV = ⅓ × Base Area × hTSA = Base Area + LSAh = heightTriangular PrismV = Base Area × hTSA = 2 × Base Area + (Perimeter × h)h = heightTetrahedronV = (√2/12) × a³TSA = √3 × a²a = edge lengthSpecial Formulas and RelationshipsImportant RelationshipsConceptFormulaDescriptionHeron's FormulaA = √[s(s-a)(s-b)(s-c)]Area of triangle when all sides known; s = (a+b+c)/2Slant Height (Cone)l = √(r² + h²)Relationship between radius, height, and slant heightDiagonal (Rectangle)d = √(l² + b²)Diagonal of rectangle using Pythagoras theoremDiagonal (Cube)d = a√3Space diagonal of cubeDiagonal (Cuboid)d = √(l² + b² + h²)Space diagonal of cuboidConversion FormulasFromToFormulaDiameterRadiusr = d/2RadiusDiameterd = 2rDegreesRadiansRadians = (π/180°) × degreesRadiansDegreesDegrees = (180°/π) × radians

From	To	Formula
Diameter	Radius	r = d/2
Radius	Diameter	d = 2r
Degrees	Radians	Radians = (π/180°) × degrees
Radians	Degrees	Degrees = (180°/π) × radians

What are the mensuration formulas in maths? How can we remember mensuration formulas?

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Shape	Area Formula	Perimeter Formula	Key Variables
Rectangle	A = l × b	P = 2(l + b)	l = length, b = breadth
Square	A = a²	P = 4a	a = side length
Triangle	A = ½ × b × h	P = a + b + c	b = base, h = height, a,b,c = sides
Right Triangle	A = ½ × base × height	P = a + b + c	Use Pythagoras: c² = a² + b²
Equilateral Triangle	A = (√3/4) × a²	P = 3a	a = side length
Parallelogram	A = b × h	P = 2(a + b)	b = base, h = height, a,b = sides
Rhombus	A = ½ × d₁ × d₂	P = 4a	d₁, d₂ = diagonals, a = side
Trapezium	A = ½ × (a + b) × h	P = a + b + c + d	a,b = parallel sides, h = height

Shape	Area Formula	Perimeter/Circumference	Key Variables
Circle	A = πr²	C = 2πr	r = radius
Semicircle	A = πr²/2	P = πr + 2r	r = radius
Sector	A = (θ/360°) × πr²	Arc length = (θ/360°) × 2πr	θ = angle in degrees
Ring/Annulus	A = π(R² - r²)	-	R = outer radius, r = inner radius
Ellipse	A = πab	P ≈ π[3(a+b) - √((3a+b)(a+3b))]	a,b = semi-major and semi-minor axes

Shape	Volume Formula	Total Surface Area	Curved Surface Area	Key Variables
Cube	V = a³	TSA = 6a²	-	a = side length
Cuboid	V = l × b × h	TSA = 2(lb + bh + hl)	-	l = length, b = breadth, h = height
Cylinder	V = πr²h	TSA = 2πr(r + h)	CSA = 2πrh	r = radius, h = height
Cone	V = ⅓πr²h	TSA = πr(r + l)	CSA = πrl	r = radius, h = height, l = slant height
Sphere	V = (4/3)πr³	TSA = 4πr²	Same as TSA	r = radius
Hemisphere	V = (2/3)πr³	TSA = 3πr²	CSA = 2πr²	r = radius

Concept	Formula	Description
Heron's Formula	A = √[s(s-a)(s-b)(s-c)]	Area of triangle when all sides known; s = (a+b+c)/2
Slant Height (Cone)	l = √(r² + h²)	Relationship between radius, height, and slant height
Diagonal (Rectangle)	d = √(l² + b²)	Diagonal of rectangle using Pythagoras theorem
Diagonal (Cube)	d = a√3	Space diagonal of cube
Diagonal (Cuboid)	d = √(l² + b² + h²)	Space diagonal of cuboid