Measure from A toward C. Finding the perpendicular aв to rise at 473, and its length 437 links; return, and continue toward C, B = till you come to the place where the second perpendicular bD rises. There note down its distance from A, 1128 links; measure bD 508 links; then complete the measuring of the diagonal to C, and let the whole be 1490 links. After this, measure the diagonal BD, for a proof-line, which you will find 1152 links. 2. In taking the dimensions of a trapezium, I found the first perpendicular to rise at 539, and to measure 725 links; the second at 1890, and to measure 832 links; the whole diagonal measured 2456 links; required the area of the trapezium. Ans. 19a. Or. 19p. 3. The first perpendicular of a trapezium rises at 467, and measures 545 links; the second at 1418, and measures 467 links; required its area, the whole diagonal being 1840 links. Ans. 9a. 1r. 9p. 4. Lay down a field, and find its area, from the following notes. 5. Required the plan and area of a field, from the following dimensions. 6. Lay down a field, and find its area, from the following notes. A field of four sides may sometimes be surveyed by dividing it into two right-angled triangles, and a trapezoid. To compute the Content. RULE.-Multiply the sum of the two perpendiculars by their distance upon the base-line, and the product will be double the area of the trapezoid. The area of each triangle must be found as before. Examples. 1. It is required to survey the annexed figure, and find its area. B E D Measure the base AD, and enter in your field-book where the two perpendiculars rise, &c., as in the following notes. 2. Required the plan and area of a field, from the following notes. 3. Lay down a field, and find its area, from the following dimensions. Fields comprehended under more than Four Straight Sides. Fields having more than four sides may be surveyed by reducing them into triangles and trapeziums. Thus, a field of five sides may be reduced into a triangle and a trapezium; of six, into two trapeziums; of seven, into two trapeziums and a triangle; of eight, into three trapeziums ; &c. The propriety of dividing fields in this manner depends entirely on the relation which the angles have to one another; it is, therefore, sometimes more accurate to divide them into triangles. To compute the Content. RULE. By the rules given in the last two problems, find the double area of each triangle and trapezium contained in the figure. Collect all the double areas into one sum, which divide by 2, and the quotient will be the whole area. Examples. 1. Lay down a field, and find its area, from the following notes. From the notes, the figure obviously consists of five sides, and is divided into a triangle and a trapezium. Draw the base AC, which D a B make 1433 links; at 643 links, let fall the perpendicular aB, upon which lay off 273 links; join AB and CB, and the triangle is E |