Question

Mr. Hewitt is hoping that Mrs. Hoffman will buy him a geometrically interesting piece of land on which he will build a castle. Mrs. Hoffman has said that she will only buy the land if it costs less than $4.00 per square foot. The plot shown below is listed for $168,240. Is Mr. Hewitt going to be able to get this land?

Answer 1

We can easily break this down into four triangles.  There will be one on the top right, bottom left and also in opposite corners.  Using the formula A = 1/2bh, we can find that the area of the four triangles are 1120, 2063, 16091 and 21689. If we add up the area of the four triangles, we get 1120 + 2063 + 18091 + 21689 = 42963 ft^2.  Since the total cost $168,240, we know the cost per square foot is 168240/42963 = $3.92.  So in other words, Mr. Hewitt will get his land, but barely.