Area of an Ellipse

In this assignment we will continue with the ideas of the assignment Areas of Leaves. Use the method of that assignment to approximate the area of the ellipse below, repeating the measurement by placing the shape on the dot paper five times (in "random" positions) and average your results.

Next, to see how the method depends on how many attempts you do, we will, as a class, calculate the average of everybody's data, filling in the following table.

Number of Trials Per PersonClass Average
1 
2 
3 
4 
5 

Compare these approximations with the actual area of an ellipse. Measure the major and minor axes of the ellipse. These are indicated in the following picture; the major axis is the longer length. Then, use the formula for the area of an ellipse given to you to find its area.

What do you conclude from this work about the accuracy of the method for approximating the area of the ellipse?