. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. the said half sum and the three remainders together; thesquare root of this product is the area required. 1. Find the area of a triangle whose sides are 20, 30, and 40. Ans. sum =45, 1st Rem. =25, 2d=15, 3d=5. <()= 2. How many acres in a triangle whose sides are severally 60,50, and 40 rods ? Ans. 6^ nearly. 3. How many square yards are there in a triangle whose sidesare 30, 40 and 50 feet ? Ans. 66f. 4. T
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. the said half sum and the three remainders together; thesquare root of this product is the area required. 1. Find the area of a triangle whose sides are 20, 30, and 40. Ans. sum =45, 1st Rem. =25, 2d=15, 3d=5. <()= 2. How many acres in a triangle whose sides are severally 60,50, and 40 rods ? Ans. 6^ nearly. 3. How many square yards are there in a triangle whose sidesare 30, 40 and 50 feet ? Ans. 66f. 4. There is a triangular lot of land containing 8 acres, two ofits sides are 64, and 46 rods respectively; what is the angle be-tween these sides, and what is the length of the remaining side ? Ans. The angle is 60° 27, or is supplement 119° side is rods, or rods ; the less angle corres-ponding to the lesser side. In short, there are two triangles answeringto the conditions, the one is ABE, the otherABC. They are equal because they are onthe same base and between the same , AC = 74 SURVEYING. PROBLEM V. To find the area of a trapezoid. Rule.— Add the two parallel sides together, and take half the this half sum by the perpendicular distance between the sides. Or, The sum of the parallel sides multiplied by their distanceasunder will give twice the area. (Leg. book IV, prop. VII. Rob. b. I, th. 31). Remark.— The application of this problem is the most important of anyin general surveying, as will appear in the sequel, and if the geometricaltheorem is not familiar to the student he should again review it. Ex. 1. In a trapezoid, the parallel sides are 750 and 1225, andthe perpendicular distance between them 1540 links: to find thearea. 1225750 1975X770=152075 square links =15 acr. 33 perches. Ex. 2. How many square feet are contained in a plank, whose length is 12 feet six inches, the breadth at the greater end 15 inch
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