Note: This activity is not in metric units since tire pressure gauges commonly use psi or pounds per square inch. Metric conversions can be made at the end if desired.
First, measure the surface area of the bottom of each tire using your thin cardboard pieces. Safety note: Remember to set the parking brake while taking these measurements! The car should be stationary during this part of the activity.
Most tire "footprints" are roughly rectangular in shape. Starting with any tire, shove a piece of cardboard under the base of the tire as far as it will go. Wedge other pieces of cardboard tightly under the other sides of the tire to define the four edges (front, back, left, right) of the tire's footprint (see image below).
Next, use a tire gauge to measure the internal air pressure of the tire (see photos below).
Carefully reposition the car so the tire is off the cardboard, then use your ruler to measure the length and the width of the empty space bounded by the pieces of cardboard (see photos below). Your measurements should be in inches.
Calculate the surface area of the part of the tire that touches the ground by multiplying the length and width of the footprint. Your answer should be in square inches.
To find the amount of weight the tire supports, multiply the surface area by the air pressure reading (psi) for that tire. When you multiply square inches by pounds per square inch, the square inches cancel and you're left with pounds. For example:
28 square inches x 30 pounds / square inch = 840 pounds
Repeat the steps above for each of the car's four tires.
Add the weight of all the tires together to get the total weight of the car.
To see how close you came to the real weight of the car, check the owner's manual or look at the specification plate on the inside of the driver's side door.