Formulas of area, perimeter and volume of various shapes

Name symbol perimeter c and area s

The length of side a of a square is c = 4a.

S=a2

The length of a side and b side of a rectangle is c = 2 (a+b).

S=ab

The length of three sides of triangle A, B and c-

Height of h-a edge

Half the circumference

A, b, c- internal angle

Where s = (a+b+c)/2s = ah/2.

=ab/2 sinC

=[s(s-a)(s-b)(s-c)] 1/2

=a2sinBsinC/(2sinA)

Quadrilateral d, d- diagonal length

α diagonal angle s = DD/2 sin α

Length of a and b sides of parallelogram

Height of h-a side

α-included angle between two sides s = ah

=absinα

A-side length of diamond

α-included angle

D- long diagonal length

D- short diagonal length s = DD/2

=a2sinα

Trapezoids a and b- length of upper and lower bottoms

up level

M- centerline length s = (a+b) h/2

=mh

radius of a circle

D- diameter c = π d = 2π r

S=πr2

=πd2/4

Sector r- sector radius

Degree of central angle

C=2r+2πr×(a/360)

S=πr2×(a/360)

Bow l- arc length

B chord length

H vector height

R radius

The degree of α-central angle S = R2/2 (π α/ 180-sin α)

= r2arccos[(r-h)/r]-(r-h)(2rh-H2) 1/2

=παR2/360-b/2[R2-(b/2)2] 1/2

=r(l-b)/2 + bh/2

≈2bh/3

Ring r- excircle radius

R- radius of inner circle

D- cylinder diameter

D- diameter of inner circle s = π (R2-R2)

=π(D2-d2)/4

Major axis of ellipse d

D- minor axis s = π DD/4

Cubic figure

Naming symbols area s and volume v

The side length of cube a is s = 6a2.

V=a3

Length of cuboid a

B width

C- height s = 2 (AB+AC+BC)

V=abc

Bottom area of prism s

H- height v = sh

The base area of the pyramid

H- height v = sh/3

Prisms S 1 and S2- upper and lower bottom areas

H- height v = h [s1+S2+(s1s1)1/2]/3.

Prisma toid s 1- Upper bottom area

S2- bottom area

S0- Cross-sectional area

H- height v = h (s 1+S2+4s0)/6.

R- base circle radius of cylinder

up level

Bottom circumference

S- bottom area

S-side-lateral area

S table-surface area c = 2π r

S bottom = π R2

S side = ch

S table = ch+2s bottom

V = s bottom h

=πr2h

R-the radius of the outer circle of the hollow cylinder.

R- radius of inner circle

H- height v = π h (R2-R2)

Radius of base circle of r- straight cone

H- height v = π r2h/3

Cone r- upper bottom radius

R- bottom radius

H- height v = π h (R2+RR+R2)/3

Sphere radius

Diameter v = 4/3 π R3 = π D2/6

Ball missing h- ball missing height

R sphere radius

A—— Radius of ball bottom v = π h (3a2+H2)/6.

=πh2(3r-h)/3

a2=h(2r-h)

Table r 1 and R2- the radius of the top and bottom of the table.

H- height v = π h [3 (r 12+R22)+H2]/6.

Circle radius

D-ring diameter

R-ring section radius

D-ring cross-sectional diameter v = 2π 2rr2

=π2Dd2/4

Barrel D- the diameter of the belly of the barrel

D- barrel bottom diameter

H- barrel height v = π h (2d2+D2)/ 12

(The bus is circular, and the center of the circle is the center of the bucket)

V=πh(2D2+Dd+3d2/4)/ 15

(The bus is a parabola)