Quandaries and Queries


I am trying to figure out how many square feet are in a piece of property. Start at Point A-then go 140 feet north-then 100 feet due east-then 300 feet at an angle southeast so that connecting to point A would be a straight line (right angle to first line north.)
I sure hope you can understand this description. I'd really appreciate it if you could tell me HOW you figure something like this.




Hi Deb,

I drew a diagram of you lot and added a perpendicular line from C to DA meeting DA at P to see that the lot can be divided into a rectangle APCB and a right triangle DCP.

The rectangular section has area 100 140 = 14 000 square feet. The area of a triangle is half the base times the height so I can calculate the area of the triangle if I can find the length of the base PD. I can find this using Pythagoras' Theorem. (It is really amazing how useful this theorem is.)

Pythagoras' Theorem for triangle DCP says

|CP|2 + |PD|2 = |DC|2

That is

1402 + |PD|2 = 3002


|PD| = Sqrt[3002 - 1402] = Sqrt[70400] = 265.33 ft

Hence the area of the triangle is

 1/2 |PD| |CP| = 1/2 265.33 140 = 18 573 square feet.

Thus the area of your property is

14 000 + 18 573 = 32 573 square feet.



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