Take a leaf or some other irregular shape. Place the leaf on a piece of centimeter dot paper. Count how many dots are covered by the leaf. Each dot represents a one square centimeter area. Therefore, the number of dots covered is an approximation to the area (in square centimeters) of the leaf. After making the count, pick up the leaf and place it down somewhere else on the paper and repeat the count. Do this a total of five times. Average your five counts. This average is then probably a reasonable estimation of the actual area of the leaf. One reason for repeating the count is to minimize the error due to how the leaf was placed on the paper.
Repeat this method with the leaf of somebody next to you. Doing so will also allow you to compare your numbers with another person measuring the same shape.
Describe the method you learned for approximating the area of any shape. Be complete but concise, and turn in your page(s) of dot paper. Make sure to say why you don't necessarily calculate the exact area, and why you count the dots covered by the shape more than once.
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Draw or trace the shapes you used, and give your calculations for these shapes.
It is not necessary to use centimeter dot paper in order to approximate the area of a figure. You can use inch dot paper, or paper with dots more frequent than each centimeter. For example, you could use paper that has dots 1 millimeter apart. The following pictures represent how an object would look when placed on centimeter dot paper and on millimeter dot paper. Which paper (of the two below) do you think would give you a better estimate of the actual area of the figure?
