EXAMPLE. 1. In a square field, A, B, C, D, each side of which measures 40 rods, or poles, how many acres? 2. In a square field, each side of which measures 35 two pole chains, how many acres? Ans. 30 acres 2 roods 20 perches. 3. A piece of square ground measures 16 perches on each side; what is the content in acres? Ans. 1 acre 2 roods 324 perches. 2d. To find the content of an oblong square piece of ground, called a parallelogram. RULE. Multiply the length by the breadth, and the product will be the answer. EXAMPLE. 1. There is an oblong square piece of ground, A, B, C, D, the longest sides of which measure 64 perches, and the shortest sides, or ends, measure 40; how many acres does it contain? 2. In a piece of ground lying in the form of an oblong square, the length measures 120 perches, and the breadth 84; what is its content in acres? Ans. 63 acres. 3. A lot of ground lying in the form of an oblong square, measures 240 feet in length, and 120 in breadth; what is its content in acres? Ans. 0 acres 2 quarters 25 perches 213 feet. 4. There is an oblong piece of ground, whose length is 14 two pole chains 25 links, and breadth 8 chains 37 links; how many acres does it contain? Ans. 3 acres 0 quarters 27 perches nearly. Note. The English statute perch is 5 yards, the two pole chain is 11 yards, or 33 feet, and is divided into 50 links; the four pole chain is 22 yards, or 66 feet, and contains 100 links; hence the length of a link in a statute chain is 7,92 inches, and 25 links make 1 rod. And consequently, if the links be multiplied by 4, carrying 1 to the chains for every 25 links, and the chains by 2, the product will be perches, and decimals of a perch. 5. An oblong piece of ground measures 17 two pole chains and 21 links in length, and 15 chains 38 links in breadth; how many acres are contained therein? Ch. L. 2 4 Ch. L. 15 38 2 4 34 84 perches, the length. 31 52 p. the breadth. Then 34,84 × 31,52=1098,1568 perches 6 acres 3 qr. 18,15+ perches. 3d. To find the content of a triangular piece of ground. RULE. Multiply the base by half the perpendicular, or the perpendicular by half the base, or take half the product of the base into the perpendicular. 1. Let A, B, C, be a triangular piece of ground, the ongest side or base B, C, is 24 chains 38 links, and perpendicular, A D, 13 chains 28 links; how many acres does it contain? Operation. Ch. L. 24 38 49,52 perches 9904 4952 34664 9904 1342,9824 Half the sum is 4,0) 67,1,4912 perches 4) 16,31 4 0 31,4 Ans. 4 acres 0 roods 31,4 perches. 2. In a triangular piece of ground, the base or longest side measures 75 perches, and the perpendicular 50; how many acres does it contain? Ans. 11 acres 2 qrs. 35 perches. 3. How much will a triangular piece of ground come to at 45 dollars per acre, the longest side or base of which measures 120 perches, and the perpendicular 84 perches. Ans. 1417 dolls. 50 cents. 4. How many superficial yards are contained in a triangular piece of ground, the base of which measures 140 feet and the perpendicular 70 feet? Ans 544 yards 4 feet. 4th. To find the content of a piece of ground, in the form of an oblique parallelogram. Let A, B, C, D, be a piece of ground in the form of un oblique parallelogram, the base of which, A, B, measures 44 perches, and the perpendicular, D, E, 40 perches; how many acres does it contain? 2. A piece of ground lying in the form of an oblique parallelogram, is found to measure 80 perches along its base, and its perpendicular height 24 perches; how many acres does it contain? Ans. 12 acres. 5th. To find the content of a piece of ground bounded by four sides, none of which are parallel or equal. RULE. Find the length of a diagonal line between the two most distant corners, and multiply this line by the sum of the two perpendiculars falling from the other corners to that diagonal line, and half the product will be the area. 1. Let A, B, C, D, be a field with four irregular and unequal sides, the diagonal line of which, A, C, measures 80 perches, the perpendicular, B, m, measures 25 perches, and the other perpendicular, D, n, 35 perches; how many acres does it contain? 80 the length of the diagonal line. 25+3560 the sum of the two perpendiculars. 2. In a field of four unequal sides, the diagonal line between the two most distant corners measures 120 rods, and the perpendiculars measure, the one 48, and the other 24 rods; required the number of acres it contains? Ans. 27 acres. 6th. To find the area of a piece of ground lying in a circle, or ellipsis. RULE. Multiply the square of the circle's diameter, or the product of the longest and shortest diameters of the ellipsis, by the decimal number ,7854, the product will give the area. Note. In any circle, the Diameter multiplied Circumference divided by 3,14159 produces the circum. quotes the diameter. |