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2D GEOMETRY FORMULAS SQUARE CIRCLE s = side r = radius, d = diameter Area: A = s2 s Diameter: d = 2r b d Perimeter: P = 4s Area: A = πr2 Circumference: C = 2πr = πd r s RECTANGLE l = length, w = width SECTOR OF CIRCLE Area: A = lw w r = radius, θ = angle in radians s Perimeter: P = 2l +2w Area: A = 1θr2 2 Arc Length: s = θr θ l r TRIANGLE b = base, h = height a c ELLIPSE Area: A = 1bh h a = semimajor axis b 2 Perimeter: P = a+b+c b = semiminor axis b a Area: A = πab b Circumference: EQUILATERAL TRIANGLE C≈π3(a+b)−p(a+3b)(b+3a) s = side Height: h = √3s s s 2 h √ Area: A = 3s2 ANNULUS 4 s r = inner radius, R=outer radius Average Radius: ρ = 1(r +R) b r PARALLELOGRAM 2 Width: w = R−r R b = base, h = height, a = side Area: A = π(R2 −r2) Area: A = bh h a or A = 2πρw Perimeter: P = 2a+2b b REGULAR POLYGON TRAPEZOID a s = side length, s a;b = bases; h = height; n = number of sides c;d = sides d Circumradius: R = 1scsc(π) b R 1 c h 2 n Area: A = (a+b)h 1 2 π 2 Area: A = 4ns cot(n) Perimeter: 1 2 2π P =a+b+c+d b or A = 2nR sin( n ) MYNCERTSOLUTIONS.COM 3D GEOMETRY FORMULAS GENERAL CONE CUBE ORPYRAMID s = side s A=area of base, h = height h Volume: V = s3 1 Volume: V = 3Ah Surface Area: S = 6s2 A s s RECTANGULAR SOLID RIGHT CIRCULAR CONE l = length, w = width, r = radius, h = height h = height h Volume: V = 1πr2h h Volume: V = lwh 3 Surface Area: Surface Area: √ 2 2 2 r w S =πr r +h +πr S =2lw+2lh+2wh l SPHERE FRUSTUMOFACONE r = radius r = top radius, R = base radius, r Volume: V = 4πr3 r h = height, s = slant height 3 Volume: V = π(r2 +rR+R2)h s Surface Area: S = 4πr2 3 Surface Area: h R S =πs(R+r)+πr2+πR2 RIGHT CIRCULAR r SQUARE PYRAMID CYLINDER r = radius, h = height s = side, h = height h Volume: V = 1s2h h Volume: V = πr2h 3 2 Surface Area: Surface Area: S = 2πrh+2πr √ 2 2 s S =s(s+ s +4h ) s R r TORUS REGULAR TETRAHEDRON r = tube radius, s = side √ s Volume: V = 1 2s3 R=torus radius 12 √ Surface Area: S = 3s2 Volume: V = 2π2r2R Surface Area: S = 4π2rR MYNCERTSOLUTIONS.COM
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