10.6.8 Estimating Complicated Areas

The ability to calculate or estimate areas occurs in many practical situations from estimating the area of a piece of land or the area of a floor or wall in a room, to minimizing the amount of packaging needed in a business. There are many other scientific and engineering applications.

In medicine, it is important to be able to estimate the surface area of different parts of the body, both for the treatment of burns and also for calculating drug doses for chemotherapy. For example, if a burn covers more than 15% of the body, the patient may suffer from shock, and it is important to quickly get the patient medical attention.

But how do you do estimate a surface area as complicated as a human body?

Example: Body Area

How could you estimate the area of part of a body or a whole body? Think of as many approaches as you can, mathematical or otherwise, and be creative! You don’t need to work out these estimates at this stage—just make suggestions on how you might do it.

In an emergency, how could you tell quickly whether a person had suffered burns on more than 15% of the body?

If there were a medical emergency, coming up with an answer an hour later such as “The area burned is 0.98562 square meters and since this is over 15% of the body area, I recommend immediate medical attention” isn’t going to help. A rough estimate will be good enough to make the decision about treatment.

One approach (that uses the mathematical modeling cycle from Unit 2) would be to approximate the body with simpler shapes such as cylinders and spheres, and then, after taking many individual measurements, determine the area of these shapes (for example, the surface area of a leg could be modeled by two cylinders).

The total surface area of the body could then be estimated by adding the areas of the individual shapes. However, there are many ways of approaching this problem, and some of these are discussed below. Which one you choose will depend on how accurate you need the answer to be and other physical considerations.

A more practical approach of solving the problem might be to wrap the body in cloth so that it covers the skin, then remove the cloth and measure the areas of the flat cloth shapes that result.

Or you might decide to do some research to see if there are any formulas for body area.

Alternatively, the area of one side of a person’s hand is estimated to be about 1% of the total body surface area. You could draw around the hand, on graph paper marked in square centimeters, and then count the squares to find the area or just estimate this area by using simple shapes. This would give an estimate for the area of the hand, and multiplying by 100 would then give an estimate of the total body area.

You could also use the hand area as an informal measure to find the area of a burn on part of the body by estimating how many handprints would cover the burn. For example, if the burn were covered by three handprints, an estimate for the area would be 3% of the total body surface area. This rough estimate could be made very quickly at the scene of the accident. Although it may not be as accurate as the earlier methods, it would enable the paramedics to make a quick decision on the urgency of the situation and possible treatments.

Paramedics also use the “rule of nines” for extensive burns on adults. This splits the body into sections with each section being either 9% (head, chest, abdomen, arm) or 18%, (leg, back) of the total body surface area. Although more accurate charts for estimating different body areas exist, the rule of nines is easy to remember and allows an estimate to be made quickly in an emergency.

10.6.7 Estimating Areas