1. Estimating Areas The art of Math

2. Exact Answers? Not Exactly… You can’t always get an exact answer But sometimes you still need to get very close to the right answer So how do you get close enough?

3. The Shape:  There is no formula for this shape  You’ll need a method to estimate the area  There is more than one way to do it  Some ways will work better than others

4. Two Methods to Estimate Area: Break the complicated shape down into simple shape you can easily find the area of, sum up those areas Create a uniform grid and count out the number of squares contained in your shape

5. First Method: Find Simple Shapes You Do Know!

6. Continue To Break The Shape Down  At this point you can easily measure the majority of the area in this shape  Is this a good enough estimate?

7. That depends, what is this for?  The red is the area we have missed  Is this a significant amount for our application?  That will decide if our estimate is good enough

8. Let’s Get More Accurate  Here is some of our “extra” space  We can continue to break that shape down just as before.  If you need you can keep going and going…

9. Getting Very Accurate Now…

10. Over vs. Underestimates: Depending on the job, you may prefer and overestimate. Sometimes you can use overestimates to make up for areas you haven’t included in your estimate.

11.  We can quickly estimate the area with a Triangle, one is an overestimate, the other is an underestimate.  Can we be more accurate with just one Triangle? How?

12.  Notice we are counting some area not in the shape, but leaving some out as well, I think we are getting pretty close

13.  What should we do now? Second Method: Grid it Up

14. Count…  What about the extra area?

15. Count it too…  Lets take a closer look…

16. It’s a Balancing Act  Count it all!  Over or Underestimate if you need to  A little of both may be even more accurate in the end…

17. Try your shape again. Are your answers close?