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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 )
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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
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