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Formula for geometrical figures

pi (p)=3.1415926535 ...

Perimeter formula

Square

4 side

Rectangle

2 (length + width)

Parallelogram

2 (side1 + side2)

Triangle

side1 + side2 + side3

Regular n-polygon

n side

Trapezoid

height (base1 + base2) / 2

Trapezoid

base1 + base2 + height [csc(theta1) + csc(theta2)]

Circle

2 pi radius

Ellipse

4 radius1 E(k,pi/2)
E(k,pi/2) is the Complete Elliptic Integral of the Second Kind
k = (1/radius1) sqrt(radius12 - radius2 2)

Area formula

Square

side2

Rectangle

length width

Parallelogram

base height

Triangle

base height / 2

Regular n-polygon

(1/4) n side2 cot(pi/n)

Trapezoid

height (base1 + base2) / 2

Circle

pi radius2

Ellipse

pi radius1 radius2

Cube (surface)

6 side2

Sphere (surface)

4 pi radius2

Cylinder (surface of side)

perimeter of circle height


2 pi radius height

Cylinder (whole surface)

Areas of top and bottom circles + Area of the side


2(pi radius2) + 2 pi radius height

Cone (surface)

pi radius side

Torus (surface)

pi2 (radius22 - radius12 )

Volume formula

Cube

side3

Rectangular Prism

side1 side2 side3

Sphere

(4/3) pi radius3

Ellipsoid

(4/3) pi radius1 radius2 radius3

Cylinder

pi radius2 height

Cone

(1/3) pi radius2 height

Pyramid

(1/3) (base area) height

Torus

(1/4) pi2 (r1 + r2) (r1 - r2)2


If l, b and h are length, breadth and height of a cuboid, then
lateral surface area = 2h (l + b)
total surface area of the cuboid = 2(lb + bh + lh)
volume = lbh

If 'a' is the length of the edge of a cube, then
lateral surface area of the cube = 4a2
total surface area of the cube = 6a2
volume = a3

Curved surface area of a cylinder (CSA) = 2prh.

Total surface area of a cylinder (TSA) = 2prh + 2pr2 = 2pr(h + r).

Volume of a cylinder (V) = pr2h.

Base area of the cone = pr2

Curved surface area of the cone = prl

Total surface area of the cone = prl + pr2 = pr(l + r)

Volume of the cone = 1 3 pr2h

Surface area of a sphere (A) = 4pr2

Volume of a sphere (V) = 4 3 pr3

Surface area of a hemisphere = 2pr2

Total surface area of a hemisphere = 3pr2

Volume of a hemisphere = 2 3 pr3




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