Area of circle: pi*r^2, where r is the radius of the circle.

Area of square: s^2, where s is the side of the square.

Area of rectangle: l*w, where l and w are the two sides.

Area of parallelogram: b*h, where b is the base and h is the height.

Area of triangle: 1/2*bh, where b is the base and h is the height.

This should start you off.

Volumes+a little bit past the basics

Volume of a cube: r^3
Volume of a rectangular prism: xyz
Volume of a sphere: 4/3 pi r^3
Volume of a cylinder: pi r^2*h
Volume of a cone: 1/3 pi r^2*h

Area of a rhombus: 1/2*x*y (x and y are the diagonals)
Area of a ellipse: 1/2*a*b (a and b are the semi-axis)
Area of a trapezoid: 1/2*h*(a+b) (a and b are the bases)

An unrelated note but interesting

The derivative of the Volume of a sphere equals its surface area

f(x)=4/3 pir^3
f'(x)=4/3(3r^2)pi=4pir^2

Surface Areas

SA of a cube: 6r^2
SA of a rectangular prism: 2xy+2yz+2xz
SA of a sphere: 4pi r^2
SA of a cone: pi*r*l+pi r^2
SA of a cylinder: d*pi*h