Problem #1: Egyptian Land Taxes In ancient Egypt, landowners paid taxes to the government, similar to today. The amount of tax owed depended on the size or area of your land. If your plot of land was a quadrilateral, the tax surveyor used the following method to calculate (the approximate) area of your land: the tax surveyor averaged both pairs of opposite sides and multiplied these two numbers to calculate the area of any quadrilateral. Note that this method will not result in the actual area of the quadrilateral in many cases. a. Use the Egyptian tax surveyor's method to calculate the (approximate) "area" of the following plot of land. 40 50 60 20 b. For what types of quadrilaterals (i.e., trapezium, kite, trapezoid, parallelogram, rhombus, rectangle, square) does the Egyptian tax surveyor's method calculate the exact area of the quadrilateral? Explain and show examples of quadrilaterals with side lengths that support your explanation. c. Does the Egyptian tax surveyor's method ever benefit the government? That is, does the method ever overestimate the area a landowner has? Explain. For what types of quadrilaterals does the method overestimate the area? List all you can think of and provide examples for each. Explain. d. Does the Egyptian tax surveyor's method ever benefit the landowner? That is, does the method ever underestimate the area a landowner has? If yes, explain what types of quadrilaterals. If no, explain why you think this method never underestimates the area.

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