Ex. The offsets taken in links are, at 124, 17; at 218, 56; at 288, 122; at 340, 96; at 378, 125; find the area of the figure. I. Find the area of an irregular piece of land from the following offsets taken in yards: at 60, 40; at 80, 54; at 90, 52; at 110, 0, Ans. 2 r. 25 P. 2. The following offsets are taken in links: at 0, 70; at 40, 75; at 66, 84; at 88, 92; at 98, 102; at 115, 108; find the area. Ans. 15 P. 3. The following offsets are taken in feet: at 0, 30; at 20, 28; at 35, 24; at 50, 20; at 64, 14; at 80, o; find the ground rent at id. per yard. Ans. 15s. 3 d. 4. Find the area of a square whose side is 334 feet. 5. Find the area of a square field whose diagonal is 7 chns. 45 lks., and the rent of the same at £2. 12s. 6d. per acre. Area, 2 a. 3 r. 4'02 p. Rent, £7. 5s. 8363d. 6. Find the area of a rectangle whose length is 5ft. 74in., and breadth 3 ft. 51 in. Ans. 1943 sq. ft. 7. Find the cost of carpeting a floor 18 ft. 6 in. long, and 14 ft. 8 in. broad, at 5s. 5d. per yard. Ans. £8. 3s. 3d. 8. Find the cost of paper for a room 21 ft. 6 in. long, 16 ft. 9 in. broad, and 9 ft. high; the paper being 20 inches wide, at 1s. 3d. per dozen. Ans. 14s. 4 d. 9. Find the area of a triangle whose base is 26 ft. 3 in. and perpendicular 12 ft. 4 in. IO. The area of a triangle is 5 a, 2 r. 8 p., is 48 poles; find the perpendicular. Ans. 1617 ft. and the base Ans. 203 yards. II. The area of a rectangular field is 4 a. 2r. 24p., and one side is 465 links; find the other side. Ans. 1 furlong. 12. The diagonal of a trapezium is 605 yards, and the perpendiculars upon it from the opposite angles are 365 and 473 yards; find the area. Ans. 52 a. Ir. 20 p. 13. 1471.6. Find the diagonal of a square which contains 4 6 square feet. 14. Find the area of a field in the form of a trapezium, whose diagonal is 165 yards, and the perpendiculars upon it 123 and 251 yards. Ans. 6 a. Ir. 20 p. 15. Find the rent of a field in the form of a trapezium, whose diagonal is 18 chns. 75 lks., and the perpendiculars it 6 chs. 54 lks. and 7 chns. 82 lks., at 12s. per rood. Area, 13 a. Ir. 34 p. Rent, £32. 6s. 23d. upon 16. The rent of a field in the form of a trapezium is £31. 45. at £3. 45. per acre, and the sum of the perpendiculars upon the diagonal is 143 yards; find the diagonal. Ans. 3 furlongs. 17. The parallel sides of a trapezoid are 6 ft. 4 in. and 7 ft. 2 in., and the distance between them 4 ft. 7 in.; find the area. Ans. 30. 11 3 sq. ft. 12 chns. 18. The parallel sides of a trapezoid are 55 links and 14 chns. 73 links, and the distance between them 10 chns. 36 links; find the area. Ans. 14 a. or. 21 p., nearly. 19. Find by duodecimals the side of a square which is equal to the areas of two squares whose sides are 7 ft. 4 in. and 8 ft. 9 in. Ans. 11 ft. 5 in. 20. On measuring a piece of ground, the following offsets were taken in yards: at 24, 18; at 40, 28; at 54, 34; at 68, 30; at 80, 16; at 100, 0. Find the area. 21. Ans. Ir. 2210P. Lay down the figure, and calculate the area from the following offsets taken in links: at 0, 120; at 126, 155; at 198, 140; at 240, 134; at 300, 0. Ans. 1 r. 20 35 P. THE TRIANGLE CONTINUED. IX. To find the area of a triangle when the three sides are given. From half the sum of the sides subtract each side separately; multiply the half sum and the three remainders together, and extract the square root. Ex. 2. Find how many acres are contained in a triangular field whose sides are 217, 404, 495 yards. 2 2 .: 558 × 341 x 154 × 63 = 2 × 72 × 9 × 11 × 312, 38720 1210) 4246 3630 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. 3r. 7 p. |