Have you ever noticed how freakishly big the arms of super hero toys are? Have you ever seen anyone made like a Barbie doll? Toy companies and graphic designers often play with the proportions of characters to make them look more unique. In this activity you will examine proportional relationships of your own toys to see what they would like if they were the same height as you are.

The first thing that we need to know is how to set up a proportion. A proportion is simply two ratios that are equal to each other. So we can set up a proportion like this:

For our activity we need to convert our own height to inches. I am 5 ft 10 inches. So I am 70 inches tall.

We then have to examine the height of our action figure/doll. For my example I am going to use a He-Man figure from the 1980s.

The picture of the figure below is the actual size of the figure. It is a 1 to 1 scale.

We can examine how we compare to He-Man by using the proportion below:

He-Man’s shoulder width He-Man’s life size shoulder width

He-Man’s height in inchesYour height

In this example we are assuming that He-Man is the same height as you only dilated down to a smaller scale. We are trying to figure out how wide his shoulders would be if he were 70 inches tall

To solve the proportion we cross multiply

2.5(70) = 6(x)

We then simplify

175 = 6x

Then we divide each side by 6

29.17 = x

So He-Man’s shoulders would be approximately 2 feet 5 inches wide. Is this realistic? Look at a measurement of 29.17 inches and see.

During this activity you will be taking your own action figure and using proportions to see how accurate it is made.

Using proportions find out the following:

  1. How long would your action figure's arms be if they were as tall as you? Show your work. Is this realistic? Are the toys arms too long or too short?
  1. How long would your action figure's legs be if they were as tall as you? Show your work. Is this realistic? Are the toys legs too long or too short?
  1. How wide would your action figure's waist be if they were as tall as you?
  1. How big around (circumference) would your action figure's waist be if they were as tall as you?
  1. How wide would your action figure's shoulders be if they were as tall as you?
  1. Are your toy’s shoulders and waist realistically proportional to each other?
  1. Choose at least two other features to examine (How big around are their arms? How long is their feet? Etc…) Are they realistically proportional?
  1. Imagine that you are an action figure/doll that is as tall as your figure. How long would your toy arms be if they were proportional to your actual height? How long would your toy legs be?
  1. Why are proportions important for toy sculptors and graphic designers?

Now let us examine our data from a graphical perspective.

  1. If your action figure were only an inch tall find the dimensions for its
  2. arm length
  3. leg length
  4. waist circumference
  5. waist diameter
  6. feet
  7. head circumference
  1. Why is it important to know these measurements for a 1 inch tall action figure? Explain your reasoning.
  2. Choose three of the measurements from number one above to complete a linear function graph for. (You must complete three separate graphs)
  3. Write an equation, a verbal description, and draw a table with at least five points listed for each of the three graphs.
  4. Interpret the slope for each graph.
  5. Interpret the y-intercept for each graph.
  6. If you wanted to double the original size of your toy to make it larger with more detail what would the dimensions be for (a) through (f) above?
  7. How could the slope be useful to a toy company?