### The Pentagon Estate

Monday, December 18th, 2017Five-star general Chester T. Hopscotch (the T standing for Tecumseh, a Shawnee chief he admired very much) decided to retire at the age of 75.

The reason general Chester T. Hopscotch waited so long to retire was that he had been looking to purchase a pentagon-shaped estate to live on – for nostalgic reasons.

His adjutant, Major Janice Crackshaw, had located a property shaped like a pentagon enclosed by rows of palms on a balmy island in the Caribbean. The property Major Janice Crackshaw found was owned by a certain Cantus Sperarum Pythagorean Society which wanted to sell the property to finance a special educational project.

Adjoining the pentagon estate, were five properties in the shape of right triangles, each respectively contiguous to a side of the pentagon estate. The triangular properties were owned and occupied by five elders of the Cantus Sperarum Pythagorean Society, their leader, the Hierophant, living in the smallest triangular property as an indication of humility.

The Cantus Sperarum Pythagorean Society was willing to sell the pentagon property to a buyer who could demonstrate signs of mathematical appreciation and perspicacity, as a neighbor without these admirable qualities would be anathema.

The buyer would have to demonstrate this mathematical appreciation and perspicacity by determining the correct price for the pentagon property – this price being five million dollars times the ratio of the area of the pentagon property to the total area of the five adjacent triangular properties belonging to the Cantus Sperarum Pythagorean Society.

The correct payment offer was to be delivered within 15 days.

Major Janice Crackshaw informed General Chester T. Hopscotch of the conditions of the purchase, who, being of a mathematical bent, was glad to also have found neighbors with a similar inclination, and immediately set about to calculate the payment offer with a pen, a slide rule and a block of yellow paper.

General Chester T. Hopscotch worked out the purchase amount in a short while.

The offer made by Major Janice Crackshaw was gladly accepted by the Pythagorean Society, which looked forward to having an erudite neighbor.

*Can you work out how much General Chester T. Hopscotch offered to pay for the pentagon estate rounded to the nearest dollar?*