Mr. Hewitt is hoping that Mrs. Hoffman will buy him a geometrically interesting piece of land on which he will build a castle. M
rs. 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?
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.
