Defining Area and triangles

Question

(a) Is the definition of “area” in your dictionary good enough to explain the meaning of the term to someone who had never heard the concept before? If not, how does it fail? Imagine you have a student with the learning disability “uni-dimensia”, where they persistently think of everything in terms of length only (e.g., they think a skinny triangle “takes up more room” than a fat one). Try to write a definition of “area” that will work even on such a student. Also be sure to distinguish area from volume.

(b) How could you compare two triangles such as those below to determine which is bigger?

Answer 1

There is quite a bit in this question. To help me I broke it down into parts. So, I first looked in a dictionary. I like dictionary.com personally. I read through all of the definitions. I then looked at how each might relate to math. Some were more difficult than others. This helped me come up with various answers to the question about the definition of area.

For the next part about the student with uni-dimensia, I looked at synonyms and what words and ideas the student might already be familiar with. Perhaps they live in a city and are familiar with city blocks and apartments and parks, perhaps they live in the suburbs or country. If you are able to find something that the student can relate to and then relate that to area it would be easier for them to understand.

As far as the third part about the two triangles, I would look at the formula for area for triangles. I’m not sure how else you could do it.