## 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

Ellipse

E(k,pi/2) is the Complete Elliptic Integral of the Second Kind

## 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

Ellipse

Cube (surface)

6 × side2

Sphere (surface)

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

Cone (surface)

Torus (surface)

## Volume formula

Cube

side3

Rectangular Prism

side1 × side2 × side3

Sphere

Ellipsoid

Cylinder

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