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What's the area? Solution

There are multiple ways one might attempt the problem. We could do a Riemann Sum, use the Trapezoidal Rule, or use Simpson's Rule. Since a typical lake would be curved, it suggests that Simpson's Rule might be the most appropriate method, although all three methods end up giving basically the same result.

Using Simpson's Rule, one would add the first distance (900), plus four times the second distance (1500), plus twice the third (1800), plus four times the fourth (2000), and so forth, alternating back and forth between two times and four times. We end with four times the next to last number (800) plus the last number (0). The entire sum is then multiplied by (1/3) and by 100 (the width of the interval), to arrive at an estimate of 8,250,000 square feet. Dividing by 43,560 square feet per acre gives a result of 189.39 acres, or 189 acres.

Using the Trapezoidal Rule gives an almost identical answer of 189.05 acres. Using rectangles, and doing a Riemann sum also gives a comparable answer.