To find the area of a figure, having a part bounded by a curve.
Draw a right line joining the extremities of the curve, then find the area of the trapezium. On the right line let fall as many perpendiculars as the several windings of the curve may require. Find their lengths, and divide their sum by the number of perpendiculars, and the quotient will be the mean breadth; which being multiplied by the length of the right line, will give the area of the curved part. This area being added to that of the trapezium will give the area of the required figure.
To measure long irregular figures.
Measure the breadth at both ends, and at several places at equal distances. Add together all these intermediate breadths, and half the two extremes, which sum multiply by the length, and divide by the number of parts for the area. If the perpendiculars, or breadths, be not at equal distances, compute all the parts separately, as so many trapezoids, and add them all together for the whole area.
Example.—The breadths of an irregular figure at five equi-distant places being 8, 2, 7, 9, 4, and the whole length 40, required the area.
8 + 4 = 12 12 ÷ 2 = 6
6 + 2 + 7 + 9 = 24
24 × 40 4 = 240. Area required.
To find the number of square acres in any of the preceding figures.[56]
Divide the superficial content in feet by 43560, and the quotient will be the number required.
To bring square chains to acres.
Of square chains strike off two decimal places to the right, and the rest of the figures will be acres.