## Area of an Irregular Polygon

Jimmy went for a 4 hour bike ride on Saturday morning. The graph below displays his speed at different times of the ride. Find the area of the polygon formed by this graph. Hint: You will need to divide this polygon into smaller sections that you know how to find the area of. There are many ways to do this, but if you need help, try checking the check boxes for suggested sections. Use the tools at the top of the window to draw in your own sections. On your own paper, show your work and find the total area of the irregular polygon.

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Area of irregular polygon = ____________

Were you able to split this polygon in sections to find it's area?
What if the graph was a curve? How could you closely approximate the area, even though the graph is curved?

I would give the students time to work on this individually (10 - 15 minutes). We would check our answer as a class, and clear up any questions that came with people getting the wrong area. I would ask the class to show examples of how the figure could have been divided. This would bring up the question I always get: "Is this right so far?" They would see that people tackled the problem in a variety of ways and we all got the same answer. I would then open up a class discussion based on the questions I posed at the bottom of the worksheet. None of these students are planning on taking calculus in high school, so it would be nice to have this discussion and tell them at the end that finding the area under a curve is a major topic in calculus. Depending on how interested the students are, this whole discussion process could take the rest of the class period (35 - 40 minutes) or it could only last for half of the period (10 - 15 minutes). -->

Kelly Harms, Created with GeoGebra

Please direct questions and comments to HCPS Mathematics Specialist Henrico County Public Schools, 2009