To find the double area of the triangle IAG. The bearings and distances of the sides, if required, might readily be obtained. For, having found the distances IA, IB, we have in the triangle IAB, two sides, and an included angle; whence the angle IAB and side AB may be found. The angle IAB applied to the bearing of IA, will give the bearing of AB. In the same manner the bearings and distances of the other sides may be found. EXAMPLE 2. Being required to calculate the area of a field, the owner of which refuses permission to go on it, I choose all the angles of the field are visible. The bearing and distance of the stations, and the bearings of the angles, from cach station, are as follow. What is the area of the field? The station G bears from the station F, N. 43° W. 20 ch. To find the area of a survey by protracting it, and dividing the plot into triangles and trapeziums. The method of doing this will be easily understood from the following example. EXAMPLE 1. Given the bearings and distances of the sides of a tract of land as follow: 1st. N. 50° E. 9.60 ch.; 2d. S. 32° E. 16.38 ch.; 3d. S. 41° W. 6.30 ch.; 4th. West, 8.43 ch.; 5th. N. 79° W. 10.92 ch.; 6th. N. 5° E. 11.25 ch.; 7th. S. 83° E. 6.48 ch.; to the place of beginning. Required the area. Fig. 75, is a plot of this survey: and by drawing the lines as in the plot, it is divided into two trapeziums AGFE, AEDF, and a triangle BDC. Measure the several bases and perpendiculars, on the same scale that was used in the protraction, and find the double areas of the triangle and trapeziums by probs. 2 and 6; the sum of these will be the double area of the survey. The following field-notes are given to protract the survey and find the area. 8. N. 38° 15' W. 8.50 CHAPTER IV. LAYING OUT AND DIVIDING LAND. PROBLEM I. To lay out a given quantity of land in a square form. RULE. Reduce the given quantity to chains or perches, and extract the square root, which will be the length of a side, of the same denomination to which the given quantity is reduced. EXAMPLES. 1. Required the side of a square that shall contain 9 A. 3 R. 28 P. 2. Required the side of a square tract of land that shall contain 325 acres. Ans. 57 chains. PROBLEM II. To lay out a given quantity of land in a rectangular form, having one side given. RULE. Divide the given content by the length of the given side, the quotient will be the length of the required side. EXAMPLES. 1. It is required to lay out 120 acres in a rectangular form, the length of one side being given, equal 100 perches. Acres. 4 480 40 1,00)192,00 192 Per. the length of the other side, 2. The length of a rectangular piece of land is 8 chains; what must be its breadth, that the content may be 5 acres? |