How to find the area of this thing?

[oceanplexian]

Ok, well my friend just moved into his new house, and gave me some info on the deed, and asked me if I was smart enough to derive the area from it.

obviously not.....

but...I was still curious how you would do such a problem, and what formula you would use for the area, so I'll ask you guys.

"Beginning on the Mill Road and at the northeast corner of the lot; thence S
04 degrees 00' 29" W, 577.67 feet to a point; thence N 82 degrees 03' 55" W,
136.00 feet to a point; thence N 05 degrees 10' 38" E, 487.93 feet to a
point; thence along a curve having a radius of 450.00 feet, a distance of
150.00 feet to the point of beginning."

any ideas?

thanks,
oceanplexian

 

[tkhunny]

Generally, the key is simply to draw it well. Once that occurs, one has only to chop it up into manageable pieces - a circle here, a triangle there, etc.

A friend of mine has a 150 year old deed that states "to the creek". In the intervening time, the creek has shifted, split, and created a small island. In this case, there are legal issues, not just arithmetic, to solve the area.

 

[soroban]

Hello, oceanplexian!

And I'm sure your friend measured his land to the nearest quarter-inch
\(\displaystyle \;\;\)and his angles to the nearest hundredth of a second.

If an airplane flew \(\displaystyle 0^o\,0'\,0.01''\) off course for a thousand miles,
\(\displaystyle \;\;\)it would miss its intended desitnation by three inches.

I may try a solution . . . after I've round the measurements to integers.

 

[TchrWill]

Ok, well my friend just moved into his new house, and gave me some info on the deed, and asked me if I was smart enough to derive the area from it.

obviously not.....

but...I was still curious how you would do such a problem, and what formula you would use for the area, so I'll ask you guys.

"Beginning on the Mill Road and at the northeast corner of the lot; thence S
04 degrees 00' 29" W, 577.67 feet to a point; thence N 82 degrees 03' 55" W,
136.00 feet to a point; thence N 05 degrees 10' 38" E, 487.93 feet to a
point; thence along a curve having a radius of 450.00 feet, a distance of
150.00 feet to the point of beginning."

The only way of solving this is to lay it out according to the survey directions.

A diagonal across the area allows you to determine the angles involved and the unnown diagonal length.

Having all the angles involved and the diagonal, the areas of the two triangles created by drawing the diagonal are easy to calculate as is the segment with the 450 ft. radius.

The length of the segment chord calculates to be 169.8 ft.

The total enclosed area is 74,758 sq.ft.