Ex. 2. Required the area of a fquare, whofe fide is 12 feet? Anf. 144 fquare feet. Ex. 3. How 6 feet 3 inches? Ex. many square feet are in a fquare, whofe fide is Anf. 39 feet in. 9 pts. 4. How many fquare yards are in a fquare court, whose fide is 80 feet? Anf. 715 yds. 5 feet 。 in. 9 pts. Ex. 5. How many fquare chains are in a field, whofe fide is I mile? Anf. 6400 fq. chains. Ex. 6. Required the area of a fquare, whofe fide is 3 chains? PROBLEM II. Plate 5. fig. 71. To find the area of a rectangle. RULE. Anf. 9 fq. ch. Multiply the length by the breadth, and the product is the area. EXAMPLE I. Required the area of a rectangle, whofe height is 3000 links, and breadth 1670 links of the English chain. 1670 3000 50,10000 square links. 4 40000 40 16,00000 Anf. 50 acres, oroods 16 poles. Here, Here, because the chain is divided into 100 links, and that 100 X 100 is 10000 (the number of square links in one square chain) and 10000 x 10 = 100000 (the number of fquare links in one acre) divide the product by 100000, the quot gives acres and decimals of an acre; and this decimal is reduced to value by multiplying by 4, by 40, by 3014. Or, instead of dividing the fquare links by 100000, cut off five decimal places towards the right hand, the integral part gives acres, and those cut off are decimals of an acre, and are reduced to value accordingly. Ex. 2. Required the area of a rectangular field, whofe fides are 5.5 and 2.54 Scots chains.} Anf. 1 acre rood 23 falls 18.72 ells. Ex. 3. Required the area of a rectangle, whofe length is 151 feet, and breadth 12 feet. Anf. 186 fquare feet. Ex 4. Required the area of a rectangle, whofe length is 10 inches, and breadth 6 inches. Anf. 60 inches. Ex. 5. Required the area of a rectangle, whofe fides are 56 feet, and 18 feet 6 inches? Anf. 1036 fquare feet. Ex. 6. Required the area of a rectangle, whose length is 16, and breadth 10 yards Anf. 168.3 yds. PROBLEM III. Plate 5. fig. 72 To find the area of a rhombus or rhomboid. RULE. Multiply the length by the perpendicular breadth, and the product is the area. EXAMPLE I. Required the area of a rhombus, whofe fide is 750 links, and one of its acute angles 60°, When one of the angles of a rhombus or rhomboid are gi ven, the area may be found by the following proportion. As rad: fine included ang. :: the prod. containing fides : area, Anf. 4 acres 3 roods 19 falls 13 ells nearly. 108000 12,96000 Ex. 2. Required the area of a rhombus, whofe length is 15 feet, and perpendicular breadth 12 feet. Anf. 180 fquare feet. Ex. 3. Required the area of a rhomboid, its length being 24, and perpendicular 14 Scots chains. Anf. 33 acres 2 roods 16 falls. Ex. 4. What is the area of a rhombus, when the fide is 1260 links, and its acute angles 54° 30' ? Anf. 12 acres 3 roods 27 falls 7 ells. Ex. 5. Required the area of a rhomboid whose fides are 3200, 2400 links of the English chain, and acute angle 304 Anf. 38 a. 1 r. 24 p. Ex. 6. Required the area of a rhomboid, when the length feet 6 inches, and perpendicular breadth 6 feet 6 inches. Anf.-328 feet. Ex. 7. How many fquare yards are in a rhombus, whose fide is 15 feet, and perpendicular height 3 feet? is 50 Anf. 5 yards 5 feet 4 inches 6 parts. PROBLEM IV. To find the fide, or the perpendicular breadth of any parallelogram, the other fide and the area being given. RULE. Divide the area by the given fide, and the quotient will be the other fide. EXAMPLE I. The area of a rectangle being 100000 square links, and one of its fides 1000 links, required the other fide. 1000) 100000 100 links, or 1 chain length, 1000 R EXAM Ex. 2. A fquare field contains 120 acres, required the length 120 acres = 12000000 fquare links. of its fide. Ex. 3. The area of a rhomboid is 63 fquare feet, and the length 10 feet. Required the perpendicular breadth. Anf. 6 feet 4.2 inches. Ex. 4. The perpendicular breadth of a rhombus is 44 feet, and area 30 fq. feet. Required the side. Anf. 7.0588 feet. Ex. 5. The area of a fquare is 6740 fquare yards. RequirAnf. 82.097 yards. Examples in this problem and in the three preceding problems prove each other. ed its fide. PROBLEM V. Plate 6. fig. 74. To find the area of a triangle, its perpendicular height and bafe be ing given. RULE. Multiply the base by half the perpendicular height, and the product will be the area. .EXAMPLE. Required the area of a triangle, whose base is 64, and perpendicular 80 feet. 64 bafe. 2)5120 2560 area. Ex. 2 How many square yards are in a triangle, whose base is 99 feet, and perpendicular 85 feet 6 inches. De |