. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. miliar 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 inches, and at the less end 11 inches ? Ans. lf$|f feet. Ex. 3. In measuring along one side AB of a quadran
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. miliar to the student he should again review it. Ex. 1. In a trapezoid, the parallel sides are 750 and 1225, andthe perpendicular distance between them 1540 links: to find thearea. 1225750 1975X770=152075 square links =15 acr. 33 perches. Ex. 2. How many square feet are contained in a plank, whose length is 12 feet six inches, the breadth at the greater end 15 inches, and at the less end 11 inches ? Ans. lf$|f feet. Ex. 3. In measuring along one side AB of a quadrangular field, that side, and the two perpendiculars let fall on it from the two opposite corners, measured as below, required the content. AP = 110 links AQ= 745 AB = 1110 CP= 352 DQ— 595 Ans. 4 acres, 1 rood, perches. Here we perceive a trapezoid and two right angled B. A chain is 4 rods, and contains 100 links; 10 squarechains make an acre. PROBLEM VI. To find the Area, of any Trapezium. Divide the trapezium into two triangles by a diagonal; then findthe areas of these triangles, and add them MENSURATION. 75 Or thus, let fall two perpendiculars on the diagonal from the othertwo opposite angles ; then add these two perpendiculars together,and multiply that sum by the diagonal, taking half the product forthe area of the trapezium. Ex. 1. To find the area of the trapezium, whose diagonal is 42,and the two perpendiculars on it 16 and 16+18= 34, its half is 42 X 17= 714 the area. Ex. 2. How many square yards of paving are in the trapezium,whose diagonal is 65 feet; and the two perpendiculars let fall on it28 and 33| feet ? Ans. 222-^ yards. When the sides of a trapezium, and two of its opposite angles aregiven, the most convenient rule for finding its area is found inproblem III. Conceive CB joined, then the whole figureconsists of two triangles and the whole areais found in the following expression(AB X ACX ) + (CD X DB X
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Keywords: ., boo, bookcentury1800, booksubjectnavigation, booksubjectsurveying
