## Body Surface Area & Circle Theorems

‘Calculate an Estimate of your Body Surface Area’  Knowledge of the human body surface area (BSA) has important applications in medical practice, in particular for the correct dosage of drugs, for cardiac index to determine heart performance, as well as design of clothes. Accurate calculations of body surface area are essential for the correct dosage calculations in the treatment of chemotherapy.

A recent study found that 3% of dosages of a chemotherapy drug contained an error because of inaccurate measurements of body surface area. These incorrect dosages included a small amount of patients given potentially lethal overdoses.

Working in small groups you are going to estimate the surface area of one of the people in your group. Then you can check your result against one of the formula used in medicine to estimate BSA.

Resources

For students requiring a structured worksheet use BSA calculation

There are also some BSA teacher notes

Description

Here follows an outline of what the task is.

Estimate the surface area of the body of your teacher. Which of the following would give the closest estimate 0.1m², 0.5m², 1m², 2m², 5m², 20m², 100m² ?

• Working in small groups make the necessary measurements to calculate the surface area of a member of your group.
• Find the total surface area, then check the calculations accuracy by comparing the value found using this formula

*where BSA is in square metres, m is the body mass in kilograms,h is the body height in metres.

## Circle theorems ‎

‘Discover and generalise the theorems about angles in circles using dynamic geometry’ This activity focusses on the important difference between a particular case and the general case. Using dynamic geometry, the aim is to construct different situations with circles, measure the angles and examine what happens with those angles as the points move dynamically within the constraints given. What would the diagram on the left look like if you dragged point A all the way round to the bottom? Would it still be the same construction? These and more questions arise from this investigation and really help with both generalising and examining the limits of a generalisation.

Resources

You will need access to a dynamic geometry package such as Cabri Geometre, Geometer’s Sketchpad or Geogebra for this investigation. The activity can be run from the angles in circles worksheet.

Example

Below is a quick screencast of ‘the arrow head’ being constructed and changing dynamically. What are the patterns? How do they change as the shape changes? (screencast has no sound)

### Description

Ensure familiarity with the dynamic geometry package being used. This includes constructing segments and polygons within circles and marking and measuring angles.
Follow the instructions in the worksheet to create the various constructions given.
Play dynamically with the constructions to look for patterns.
Generalise about the phenomena noticed.

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