Not-So-Bland Land Problems
Note: Sometimes old-but-not-olde math texts include some problems involving some interesting ideas. Consider these from a text designed for engineering students.
Problem 1: A plot of land has the shape of a quadrilateral whose sides, in order, are 3,470, 1,980, 2,540, and 3,720 ft. If the last two sides form a right angle, find the area of the plot in acres.
Problem 2: A farmer traced the map of his farm on a sheet of No. 4 zinc and cut out the outline of his map. Then, to the same scale (1 in. = 50 ft), he cut out a 4-in. square. The 4-in. square weighed 1/2 oz, while the zinc map weighed 3 lb 10 1/2 oz. How many acres were there in the farm?
Source: H. Rice & R. Knight's Technical Mathematics With Calculus, 1966
Hint: For Problem 1, draw a picture....what can you find? Now, how to use that to solve for area (Hint: Think Heron's Formula).
As to the second problem, what assumptions are being made...and how can you that assumption to calculate an area (in square inches or feet)?
Solution Commentary: You can do it...you do not need further hints...