# Perimeter, Area, and Volume – Important Formula

1. The perimeter of a polygon (or any other closed curve, such as a circle) is the distance around the outside.

2. The area of a simple, closed, planar curve is the amount of space inside.

3. The volume of a solid 3D3D shape is the amount of space displaced by it.

#### 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 – radius22)

#### 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

Close