A five-sided parcel whose southerly boundary is a circular arc. Compute the area of the chord polygon by coordinates, add the circular segment R²/2·(Δ − sin Δ), and check the segment as sector minus triangle.
Apply· about 22 minutes by hand· 5 steps
Given
Parcel: LOT 6, MILLRACE ADDITION. Corners on a local plane grid, US survey feet, northing first.
A N 2500.00 E 3000.00
B N 2500.00 E 3450.00
C N 2160.00 E 3560.00
D N 1849.64 E 3380.82
E N 1980.00 E 3000.00
The boundary from C to D is not a straight line. It is a circular arc of radius R = 500.00 ft and central angle Δ = 42°00′00″, concave toward the parcel, so the arc bulges outward beyond the chord C-D.
The four remaining boundaries A-B, B-C, D-E and E-A are straight.
The coordinates given for C and D are the ends of the arc, i.e. the ends of its long chord.
Required
The area of the parcel including the ground between the chord C-D and the arc.
The answer in square feet and acres, with the segment contribution stated separately.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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