There are many geometric formulas, and they relate height, width, length, or radius, etc, to perimeter, area, surface area, or volume, etc. Some of the formulas are rather complicated, and you hardly ever see them, let alone use them. But there are some basic formulas that you really should memorize, because it really is reasonable for your instructor to expect you to know them.
For instance, it is very easy to find the area A of a rectangle: it is just the length l times the width w:
The "rect" in the formula above is a subscript, indicating that the area "A" being found is that of a rectangle. Because I'm going to be discussing area, volume, etc, formulas for different shapes, I'm using the subscripts to make clear the shape to which the particular formula refers (while using "A" for "area", "SA" for "surface area", "P" for "perimeter", and "V" for "volume"). Subscripting of this sort can be a useful technique for making your meaning clear, so try to keep this in the back of your mind for possible future use.
If you look at a picture of a rectangle, and remember that "perimeter" means "length around the outside", you'll see that a rectangle's perimeter P is the sum of the top and bottom lengths l and the left and right widths w:
Squares are even simpler, because their lengths and widths are identical. The area A and perimeter P of a square with side-length s are given by:
You should know the formula for the area of a triangle; it's easy to memorize, and it tends to pop up unexpectedly in the middle of word problems. Given the measurements for the base b and the height h of the triangle, the area A of the triangle is:
Of course, the perimeter P of the triangle will just be the sum of the lengths of the triangle's three sides.
You should know the formula for the circumference C and area A of a circle, given the radius r:
("π" is the number approximated by 3.14159 or the fraction 22/7)
Remember that the radius of a circle is the distance from the center to the outside of a circle. In other words, the radius is just halfway across. If they give you the length of the diameter, being the length of a line through the middle going all the way across the circle, then you'll first have to divide that value in half in order to apply the above formulas.