Saturday, May 28, 2011

Genealogy Fun with Math

Last night a member of one of my mailing lists posed a math question. I used to be a high school math teacher, and I knew it was solvable, as did many list members. And many of us came up with about the same answer, but I took it as a personal challenge to figure out the exact methodology. It just bugged me that I couldn't do something at 50+ that I could do in no time in my 20's. Sigh....

The problem was to find the acreage of a piece of land measuring 160 feet on one side and 250 feet on the other. There is a right angle between these two. The other sides measured 260 feet and 50 feet.

First, I used graph paper to get a decent idea what the shape looked like. Then I divided it into two triangles. It looks about like this:
We need to figure out the area of both triangles and add.  The lower triangle is easy. Use the standard formula for the area of a triangle. A = 1/2 the base times the height where the height is perpendicular to the base. So the area of the lower triangle is 1/2 * 250 * 160, or 20000 sq. feet.

Next, we can figure out the length of C with the good ol' Pythagorean theorem.  This one I remembered all by myself.

C2=A2 + B2   or
C2=(160*160)+(250*250) or

Using the handy Windows calculator, the square root of 88100 is  296.82 (rounded). So now we know the length of C. (Do NOT ask me how to do square roots by hand. There was time when I could do so, but I now consider it totally irrelevant.)

So, the sides of our mystery upper triangle are 260,50, and 296.82

Next there is the handy dandy Heron's formula (which I had to look up) that allows you to calculate the area of a triangle if you know the three sides. Again, I will cheat and use an online calculator. Read all you want to about Heron's formula and feel free to calculate by hand if you wish. I'm lazy. The area (rounded) of our second triangle is 4689.91 square feet.

Adding the two together, you get 24689.91 square feet.

And cheating again by using an online calculator, this is .57 (rounded) acres.

Admittedly, I got the same answer last night by guesstimating, but I didn't understand what I was doing. Now I do.

This was fun. (Yes, I know I'm a geek.) If you have any more math genealogy questions, put them in the comments. I'll see if the brain cells still work.

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