calculating acreage with a curve front

[Carol.Presutti@QRealEstat]

I have a 5 sided lot. Measurements are as follows: Commencing at point marking the northwestly corner of land; thence S. 1 degree 57'40" (99.41') to another point in the westerly line of the said land; thence N. 82 degrees 06' 52" W. (460.43') to a point in the easterly street line; thence northerly on a curve to the right, a radius 935.43' , for (253.85') to a point in the easterly street line; thence N. 3 degrees 07' 30" E. (104.65') to a point in the easterly street line; thence S. 82 degrees 50'14" for (390') to a point in the westerly line of Lot 8; thence S. 17 degrees 48'20" E (285.6') to the point or place of the beginning. Can you calculate area - I am looking for the square footage as exact as possible. Thank you.

[Guest]

I have a 5 sided lot. Measurements are as follows: Commencing at point marking the northwestly corner of land; thence S. 1 degree 57'40" (99.41') to another point in the westerly line of the said land; thence N. 82 degrees 06' 52" W. (460.43') to a point in the easterly street line; thence northerly on a curve to the right, a radius 935.43' , for (253.85') to a point in the easterly street line; thence N. 3 degrees 07' 30" E. (104.65') to a point in the easterly street line; thence S. 82 degrees 50'14" for (390') to a point in the westerly line of Lot 8; thence S. 17 degrees 48'20" E (285.6') to the point or place of the beginning. Can you calculate area - I am looking for the square footage as exact as possible. Thank you.

This is a tough problem. If you need an "official" answer you should really consult a surveyor, which I'm not.

Basically, the curve gives six sides. The curve has to be replaced with a calculated straight segment, and calculate the area of the six-sided figure, then adjust for the difference between the curve and the line segment.

The bearings are essential to figuring the problem. Note that the first line (99.41') and next to last line (390') are incomplete bearings as they are not specified east or west. Also could you check the bearing of last line (285.6')? If it bears to SE, then point of beginning is NOT the NW corner.

On the curved segment, is it tangent to the road bearing of N. 3 degrees 07' 30" E at the northerly end? I know it is a different lot, but what is the road bearing at the southerly end of the curve? Am I Correct that the center lies off to the east somewhere, so that a straight line between endpoints of the curve lies in the road, not the lot?

If you can answer these questions, I'll try, but if you need an answer with legal standing, you really need to consult a surveyor.

[Guest]

The curve is the eay part. The problem is usually referred to as "sector and segment of a circle" in any geometry text.

The total circumference of a 935.43' foot radius circle is 2*pi times that number and represents 360 degrees. The 253.85' arc represents 15.5485 degrees, and the half angle, 7.77425 degrees or 7 degrees 46' 27"

The straight line segment across the ends of the arc has a length 253.07' and bears N 4 degrees 38' 57 W (based on road bearing at north end and half angle). At the south end, the road should bear n 12 degrees 25' 24" W.

The area between the arc and the straight line segment is 1451.91 sq ft which should be subtracted as it lies outside the lot.

With the substitution of the straight line segment, you may already be able to calculate the 6 sided figure once you correct the bearing angles as above.