2D GEOMETRY FORMULAS - WordPress.com

2D GEOMETRY FORMULAS

SQUARE s = side Area: A = s2 Perimeter: P = 4s

CIRCLE r = radius, d = diameter Diameter: d = 2r Area: A = πr 2 Circumference: C = 2πr = πd

s s

RECTANGLE l = length, w = width Area: A = lw Perimeter: P = 2l + 2w

w l

TRIANGLE b = base, h = height Area: A = 12 bh Perimeter: P = a + b + c

a

Area: A =

d

r

SECTOR OF CIRCLE r = radius, θ = angle in radians Area: A = 12 θr 2 Arc Length: s = θr

s θ r

ELLIPSE

c

h

a = semimajor axis b = semiminor axis Area: A = πab

b EQUILATERAL TRIANGLE s = side √ Height: h = 23 s

b

s

b a

b

Circumference:   p C ≈ π 3(a + b) − (a + 3b)(b + 3a) s

h

√ 3 2 4 s

s PARALLELOGRAM b = base, h = height, a = side Area: A = bh Perimeter: P = 2a + 2b

a

h

ANNULUS r = inner radius, R = outer radius Average Radius: ρ = 21 (r + R) Width: w = R − r Area: A = π(R2 − r 2 ) or A = 2πρw

b

r

R

b TRAPEZOID a, b = bases; h = height; c, d = sides Area: A = 21 (a + b)h Perimeter: P = a+b+c+d

a c

d

h b

REGULAR POLYGON s = side length, n = number of sides Circumradius: R = 12 s csc( πn ) Area: A = 41 ns2 cot( πn ) or A = 21 nR2 sin( 2π n )

s b

R

3D GEOMETRY FORMULAS GENERAL CONE OR PYRAMID A = area of base, h = height Volume: V = 13 Ah

CUBE s

s = side Volume: V = s3 Surface Area: S = 6s2

h A

s s

RECTANGULAR SOLID l = length, w = width, h = height Volume: V = lwh Surface Area: S = 2lw + 2lh + 2wh

RIGHT CIRCULAR CONE h

w

r = radius, h = height Volume: V = 13 πr 2 h Surface√Area: S = πr r 2 + h2 + πr 2

h r

l

SPHERE r = radius Volume: V = 43 πr 3 Surface Area: S = 4πr 2

RIGHT CIRCULAR CYLINDER r = radius, h = height Volume: V = πr 2 h Surface Area: S = 2πrh + 2πr 2

FRUSTUM OF A CONE r = top radius, R = base radius, h = height, s = slant height Volume: V = π3 (r 2 + rR + R2 )h Surface Area: S = πs(R + r) + πr 2 + πR2

r

r

r s h

R

SQUARE PYRAMID h

s = side, h = height Volume: V = 13 s2 h Surface Area: √ S = s(s + s2 + 4h2 )

h s s

R TORUS r = tube radius, R = torus radius Volume: V = 2π 2 r 2 R Surface Area: S = 4π 2 rR

r REGULAR TETRAHEDRON s = side √ 3 1 2s Volume: V = 12 √ Surface Area: S = 3s2

s