Ex. 2. Find how many acres are contained in a tri angular field whose sides are 217, 404, 495 yards. .. 558-217=341 = 11 × 31, 558-404154 = 2 × 7 × 11, 558-495 63=7×9; 558 × 341 × 154 × 63 = 2a × 72 × 9o × 11 × 313, 4840) 42966 (8 a. 3 r. 204p. Ans. 1210) 4246 616 40 2464 242 44 [As an exercise on this example, the student may verify any of the results in Table II.] EXAMPLES. I. Find the area of a triangle whose sides are 22, 24, 30 chains. Ans. 26 a. or. 15 p. 2. The sides of a triangle are 1264, 1346, 1432 links; find the area. Ans. 7 a. 3 r. 73 p. 3. Find by duodecimals the area of a triangle whose sides are 4 ft. 7 in., 11 ft. 4 in., 15 ft. 3 in. Ans. 15 feet. 4. Find the area and the rent of a triangular field whose sides are 71, 81, and 103 chains, at 45s. per acre. Area, 3 a. or. 132 p. Rent, £6. 18s. 10ld. 5. ABCD is a trapezium, of which the diagonal AC is 325 yards, and the sides AB, BC, CD, DA are 123, 208, 116, 231 yards, respectively; find the area. Ans. 2 a. 3 r. 28.12 p. SIMILAR RECTILINEAR FIGURES. X. The like sides of similar rectilineal figures are proportional. The areas of similar rectilineal figures are to one another as the squares of their like sides. Ex. I. The sides of a triangle are 15, 28, 41 feet, and the area is 126 feet; find the sides of a similar triangle whose area is 56 feet. 126 56 15 102; one side is 10 feet; and by proportion, 15 28 10 183, 15 41: 10:27. Hence the three sides are 10 ft., 18 ft. 8 in., 27 ft. 4 in. Ex. 2. The sides of a rectangle are as 11 to 7, and the area is 616; find the sides. 77: 616 :: 112: 968. .. √(968)=31*112, the greater side; and by proportion, the lesser side. Ex. 3. 11 : 7 :: 31112 : 19'798, The area of a rhombus is 978 square feet, and the side is 37 ft. 2 in.; find the dimensions of a similar rhombus which shall contain 55017 square feet. = First 97837% 26 feet, the breadth of the given rhombus. 978155012 (37%): (27%); therefore the side of the required rhombus is 27 ft. 10 in.; and by proportion, 37: 277 :: 26: 193; .. the breadth is 19 ft. 9 in. EXAMPLES. I. The sides of a triangle are 25, 51, 74, and the area is 300; find the sides of a similar triangle whose area is 213313. Ans. 663, 136, 1971. 2. The sides of a rectangle are in the ratio of 2 to 3, and the area is 6 a. 2 r. 37 p. ; find the sides. Ans. 670, 1005 links. 3. The area of a parallelogram is 104 square feet, and one side is 14 ft. 3 in.; find the dimensions of a similar parallelogram whose area is 235 square feet. Side, 21 ft. 4 in. Breadth, 11 feet. 4. The base and perpendicular of a right-angled triangle are 28 and 45; find the sides of a similar triangle whose area is 4480. Ans. 743, 120. 5. The parallel sides and breadth of a right-angled trapezoid are as the numbers 4, 3, 2, and the area is 12 a. 2 r. 23 p.; find the dimensions. Sides, 374, 280 yds. Breadth, 187 yds. 6. The sides of a triangle are 7, 12, 17 chains; find the area, and deduce the area of a similar triangle whose greatest side is 59 chains. Ans. 3 a. Ir. 31 p. and 41 a. 2 r. 21 p. THE CIRCLE. XI. To find the circumference of a circle. Multiply the diameter by 3. Note. The circumference divided by 3 gives the dia |
