Trace on a white sheet of paper the boundaries of the area of the United States shown in...

Trace on a white sheet of paper the boundaries of the area of the United States shown in the accompanying diagram.

a. Use the trapezoidal rule to determine the total area.

b. Approximate the total area by breaking it into small squares. Count the number of total squares and add what you think is an appropriate value for the remaining area. Compare your findings to part (a).

c. Use an analytical balance from a chemistry lab to weigh an sheet of paper. Record the dimensions of the paper. Draw the boundaries of the area shown on the accompanying figure and cut around the boundary of the area. Determine the weight of the piece of paper that has the area drawn on it. Compare the weights and determine the area of the given profiles. What assumptions did you make to arrive at your solution? Compare the area computed in this manner to your results in parts (a) and (b). Are there any other ways that you could have determined the area of the profile? Explain.